area - Number of square units covering the shape

4 rectangular strips of wood, each 30 cm long and 3 cm wide, are arranged to form the outer section

4 rectangular strips of wood, each 30 cm long and 3 cm wide, are arranged to form the outer section of a picture frame. Determine the area inside the wooden frame.
Area inside forms a square, with a length of 30 - 3 - 3 = 24. We subtract 3 twice, because we account for 2 rectangular strips with a width of 3.
Area of a square is side * side. So we have 24 * 24 = [B]576cm^2[/B]

9 workers were hired to harvest potatoes from a field. each is given a plot which is 11*7 feet in si

9 workers were hired to harvest potatoes from a field. each is given a plot which is 11*7 feet in size. what is the total area of the field
The area of each plot is 11*7 = 77
With 9 workers, the total area of the field is:
9 * 77 = [B]693 sq feet[/B]

A bag of fertilizer covers 300 square feet of lawn. Find how many bags of fertilizer should be purch

A bag of fertilizer covers 300 square feet of lawn. Find how many bags of fertilizer should be purchased to cover a rectangular lawn 290 feet by 150 feet.
The area of a rectangle is length * width, so we have:
A = 290 * 150
A = 43,500 sq ft.
Now, to find the number of bags needed for a 300 square feet per bag of fertilizer, we have:
Bags Needed = Total Square Feet of Lawn / Square Feet covered per bag
Bags Needed = 43,500 / 300
Bags Needed = [B]145[/B]

A cubicle is 6 1?2 feet by 8 3?4 feet. What is the area of the cubicle?

A cubicle is 6 1?2 feet by 8 3?4 feet. What is the area of the cubicle?
Area of a cube is length times width:
A = 8 & 3/4 * 6 & 1/2
We need to convert these to improper fractions.
[LIST]
[*]8 & 3/4 [URL='https://www.mathcelebrity.com/fraction.php?frac1=8%263%2F4&frac2=3%2F8&pl=Simplify']converted to an improper fraction[/URL] is 35/4
[*]6 & 1/2 [URL='https://www.mathcelebrity.com/fraction.php?frac1=6%261%2F2&frac2=3%2F8&pl=Simplify']converted to an improper fraction[/URL] is 13/2
[/LIST]
Multiply the improper fractions together:
A = 35/4 * 13/2
[URL='https://www.mathcelebrity.com/fraction.php?frac1=35%2F4&frac2=13%2F2&pl=Multiply']Using our fraction multiplier[/URL], we get:
[B]455/8 sq ft[/B]
If you want to convert this to a mixed fraction, we [URL='https://www.mathcelebrity.com/fraction.php?frac1=455%2F8&frac2=3%2F8&pl=Simplify']type this in our calculator [/URL]and get:
[B]56 & 7/8 sq ft[/B]

A diving board is 10 feet long and 1 foot wide. What is its area?

A diving board is 10 feet long and 1 foot wide. What is its area?
A diving board is a rectangle. And the area of a rectangle is:
A = lw
Plugging in our numbers, we get:
A = 10(1)
A = [B]10 sq feet[/B]

A dog on a 20-foot long leash is tied to the middle of a fence that is 100 feet long. The dog ruined

A dog on a 20-foot long leash is tied to the middle of a fence that is 100 feet long. The dog ruined the grass wherever it could reach. What is the area of the grass that the dog ruined.
The leash forms a circle where the dog can get to.
A = pi(r)^2
A = 3.1415(20)^2
A = 3.1415 * 400
A = 1256 square feet
The fence blocks off half the circle where the dog can move to, so we have a half-circle area:
A = 1256/2
A = [B]628 square feet[/B]

A family room measures 15.6 feet long and 18.4 feet wide. What is the area of the room?

A family room measures 15.6 feet long and 18.4 feet wide. What is the area of the room?
The room is rectangular. So our area A = lw.
Using our [URL='https://www.mathcelebrity.com/rectangle.php?l=15.6&w=18.4&a=&p=&pl=Calculate+Rectangle']rectangle calculator[/URL], we get:
A = [B]287.04 square feet[/B]

A farmer has 165 feet of fencing material in which to enclose a rectangular grazing area. He wants t

A farmer has 165 feet of fencing material in which to enclose a rectangular grazing area. He wants the length x to be greater than 50 feet and the width y to be no more than 20 feet. Write a system to represent this situation.
Perimeter of a rectangle:
P = 2l + 2w
We have P = 165 and l = x --> x>50 and width y <= 20. Plug these into the perimeter formula
[B]165 = 2x + 2y where x > 50 and y <= 20[/B]

A flower bed is to be 3 m longer than it is wide. The flower bed will an area of 108 m2 . What will

A flower bed is to be 3 m longer than it is wide. The flower bed will an area of 108 m2 . What will its dimensions be?
A flower bed has a rectangle shape, so the area is:
A = lw
We are given l = w + 3
Plugging in our numbers given to us, we have:
108 = w(w + 3)
w^2 + 3w = 108
Subtract 108 from each side:
w^2 + 3w - 108 = 0
[URL='https://www.mathcelebrity.com/quadratic.php?num=w%5E2%2B3w-108%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']Type this problem into our search engine[/URL], and we get:
w = (9, -12)
Since length cannot be negative, w = 9.
And l = 9 + 3 --> l = 12
So we have [B](l, w) = (12, 9)[/B]
Checking our work, we have:
A = (12)9
A = 108 <-- Match!

A framed print measures 80cm by 65cm. The frame is 5cm wide. Find the area of the unframed print

A framed print measures 80cm by 65cm. The frame is 5cm wide. Find the area of the unframed print.
We subtract 5 cm from the length and the width to account for the frame:
Unframed Length: 80 - 5 = 75
Unframed Width: 65 - 5 = 60
Area of the unframed rectangle is:
A = lw
A = 75(60)
A = [B]4,500 sq cm[/B]

A Government antipollution spokeperson asserts that more than 80% of the plants in the Glassboro are

A Government antipollution spokeperson asserts that more than 80% of the plants in the Glassboro area meet the antipollution standards. An antipollution advocate does not believe the government claim. She takes a random sample of published data on pollution emission for 64 plants in the area and finds that 56 plants meet the pollution standards. Do the sample data support the government claim at the 1% level of significance?
(H0: ρ=0.8; H_{a}: ρ>0.8)
[URL='http://www.mathcelebrity.com/proportion_hypothesis.php?x=+56&n=64&ptype==&p=+0.8&alpha=+0.01&pl=Proportion+Hypothesis+Testing']Perform a hypothesis testing of a proportion[/URL]
[B]Accept null hypothesis[/B]

A kitchen measures 5 yd by 6 yd. How much would it cost to install new linoleum in the kitchen if th

A kitchen measures 5 yd by 6 yd. How much would it cost to install new linoleum in the kitchen if the linoleum costs $2 per square foot?
The kitchen has an area of 5yd x 6yd = 30 sq yards.
If the linoleum costs $2 per square foot, we have 30 sq yards / $2 per square foot = [B]$15[/B]

a painter is painting a circular sculpture. The sculpture has a radius of 5 meters. How much paint s

a painter is painting a circular sculpture. The sculpture has a radius of 5 meters. How much paint should she use to paint the sculpture
Area of a circle (A) is:
A = ?r²
Substituting r = 5 into this formula, we get:
A = ? * 5²
A = [B]25?[/B]

A playing card is 7 centimeters wide and 10 centimeters tall. What is its area?

A playing card is 7 centimeters wide and 10 centimeters tall. What is its area?
A playing card has a rectangle shape, so the area is l x w.
A = l x w
A = 10 cm x 7 cm
A =[B] 70 cm^2[/B]

A pool is 5 meters wide and 21 meter long what is the area of the pool?

A pool is 5 meters wide and 21 meter long what is the area of the pool?
A pool is a rectangle. So the area for a rectangle is:
A = lw [I]where l is the length and w is the width.[/I]
[URL='https://www.mathcelebrity.com/rectangle.php?l=21&w=5&a=&p=&pl=Calculate+Rectangle']Plugging in our width of 5 and length of 21 to our rectangle calculator[/URL], we get:
A = [B]105 m^2[/B]

A postcard is 4 inches tall and 5 inches wide. What is its area?

A postcard is 4 inches tall and 5 inches wide. What is its area?
A postcard is a rectangle. The area is 4 x 5 = [B]20 square inches[/B]

a rectangle has a length of x-7 and a width of x + 5. Write an expression that represents the area o

a rectangle has a length of x-7 and a width of x + 5. Write an expression that represents the area of the rectangle in terms of x.
Area of a rectangle (A) with length(l) and width (w) is expressed as follows:
A = lw
Plugging in our values given above, we have:
[B]A = (x - 7)(x + 5)[/B]

a rectangle has an area of 238 cm 2 and a perimeter of 62 cm. What are its dimensions?

a rectangle has an area of 238 cm 2 and a perimeter of 62 cm. What are its dimensions?
We know the rectangle has the following formulas:
Area = lw
Perimeter = 2l + 2w
Given an area of 238 and a perimeter of 62, we have:
[LIST=1]
[*]lw = 238
[*]2(l + w) = 62
[/LIST]
Divide each side of (1) by w:
l = 238/w
Substitute this into (2):
2(238/w + w) = 62
Divide each side by 2:
238/w + w = 31
Multiply each side by w:
238w/w + w^2 = 31w
Simplify:
238 + w^2 = 31w
Subtract 31w from each side:
w^2 - 31w + 238 = 0
We have a quadratic. So we run this through our [URL='https://www.mathcelebrity.com/quadratic.php?num=w%5E2-31w%2B238%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic equation calculator[/URL] and we get:
w = (14, 17)
We take the lower amount as our width and the higher amount as our length:
[B]w = 14
l = 17
[/B]
Check our work for Area:
14(17) = 238 <-- Check
Check our work for Perimeter:
2(17 + 14) ? 62
2(31) ? 62
62 = 62 <-- Check

A rectangular football pitch has its length equal to twice its width and a perimeter of 360m. Find i

A rectangular football pitch has its length equal to twice its width and a perimeter of 360m. Find its length and width.
The area of a rectangle (A) is:
A = lw --> where l is the length and w is the width
We're given l = 2w, so we substitute this into the Area equation:
A = (2w)w
A = 2w^2
We're given the area of the pitch is 360, so we set:
2w^2 = 360
We [URL='https://www.mathcelebrity.com/1unk.php?num=2w%5E2%3D360&pl=Solve']type this equation into our search engine[/URL], follow the links, and get:
w = [B]6*sqrt(5)
[/B]
Now we take this, and substitute it into this equation:
6*sqrt(5)l = 360
Dividing each side by 6*sqrt(5), we get:
l = [B]60/sqrt(5)[/B]

A rectangular garden is 5 ft longer than it is wide. Its area is 546 ft2. What are its dimensions?

A rectangular garden is 5 ft longer than it is wide. Its area is 546 ft2. What are its dimensions?
[LIST=1]
[*]Area of a rectangle is lw. lw = 546ft^2
[*]We know that l = w + 5.
[/LIST]
Substitute (2) into (1)
(w + 5)w = 546
w^2 + 5w = 546
Subtract 546 from each side
w^2 + 5w - 546 = 0
Using the positive root in our [URL='http://www.mathcelebrity.com/quadratic.php?num=w%5E2%2B5w-546%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic calculator[/URL], we get [B]w = 21[/B].
This means l = 21 + 5.
[B]l = 26[/B]

A rectangular hotel room is 4 yards by 5 yards. The owner of the hotel wants to recarpet the room wi

A rectangular hotel room is 4 yards by 5 yards. The owner of the hotel wants to recarpet the room with carpet that costs $76.00 per square yard. How much will it cost to recarpet the room? $
The area of a rectangle is length * width, so we have:
A = 5 yards * 4 yards
A = 20 square yards
Total cost = Cost per square yard * total square yards
Total Cost = $76 * 20
Total Cost = [B]$1520[/B]

A school wants to buy a chalkboard that measures 1 yard by 2 yards. The chalkboard costs $27.31 per

A school wants to buy a chalkboard that measures 1 yard by 2 yards. The chalkboard costs $27.31 per square yard. How much will the chalkboard cost?
Area of a chalkboard is denoted as :
A = lw
Given 1 yard width and 2 years length of the chalkboard, we have:
A = 2(1)
A = 2 square yards
Therefore, total cost is:
Total Cost = $27.31 * square yards
Total Cost = $27.31(2)
Total Cost = [B]$54.62[/B]

A square has a perimeter of 24 inches. What is the area of the square?

A square has a perimeter of 24 inches. What is the area of the square?
Perimeter of a square = 4s where s = the length of a side. Therefore, we have:
4s = P
4s = 24
Using our equation solver, [URL='https://www.mathcelebrity.com/1unk.php?num=4s%3D24&pl=Solve']we type in 4s = 24[/URL] and get:
s = 6
The problems asks for area of a square. It's given by
A = s^2
Plugging in s = 6, we get:
A = 6^2
A = 6 * 6
A = [B]36
[/B]
Now if you want a shortcut in the future, type in the shape and measurement you know. Such as:
[I][URL='https://www.mathcelebrity.com/square.php?num=24&pl=Perimeter&type=perimeter&show_All=1']square perimeter = 24[/URL][/I]
From the link, you'll learn every other measurement about the square.

A standard volleyball court has an area of 1800ft. The length is 60. What is the width of the volley

A standard volleyball court has an area of 1800ft. The length is 60. What is the width of the volleyball court
Plugging [URL='https://www.mathcelebrity.com/rectangle.php?l=60&w=&a=1800&p=&pl=Calculate+Rectangle']this into our rectangle calculator[/URL] and we get:
w = [B]30[/B]

A train ticket is 8 centimeters tall and 10 centimeters long. What is its area?

A train ticket is 8 centimeters tall and 10 centimeters long. What is its area?
The ticket is a rectangle. The area is:
A = lw
Plugging in our numbers, we get:
A = (8)(10)
A = 80

A triangular garden has base of 6 meters amd height of 8 meters. Find its area

A triangular garden has base of 6 meters amd height of 8 meters. Find its area
Area (A) of a triangle is:
A = bh/2
Plugging in our numbers, we get:
A = 6*8/2
A = [B]24 square meters[/B]

A yard with dimensions of 15m x 10m has a flower garden in the middle. The flower garden has a dimen

A yard with dimensions of 15m x 10m has a flower garden in the middle. The flower garden has a dimensions of 4m x 7m. What Is the area of the yard without the flower garden?
Find the area of the yard:
AY = l x w
AY = 15 x 10
AFY= 150
Find the area of the flower garden:
AFG = l x w
AFG = 7 x 14
AFG = 28
Take the area of the remaining piece of the flower garden:
ARP = AY - AFG
A = 150 - 28
[B]A = 122[/B]

Anne wants to make a platform that is 7 feet wide and 10 feet long. If she uses boards that measure

Anne wants to make a platform that is 7 feet wide and 10 feet long. If she uses boards that measure 6 inches wide by 2 feet long, how many boards will she need to complete the job?
Area of platform which is a rectangle:
A = lw
A = 10 * 7
A = 70
Area of boards which are rectangles:
A = lw
A = 2 * 6
A = 12
We divide our platform area by our board area to get the number of boards needed:
Boards needed = Platform Area / Board Area
Boards needed = 70/12
Boards needed = 5.83333
We round up if we want full boards to be [B]6[/B]

Annulus

Calculates the area of an annulus and the equation of the annulus using the radius of the large and small concentric circles.

Arc Length and Area of a Sector of a Circle

Calculates the arc length of a circle and the area of the sector of a circle

Area Conversions

This calculator converts between the following area measurements:

acre

hectare

square inch

square foot

square yard

square mile

square millimeter

square meter

square kilometer

acre

hectare

square inch

square foot

square yard

square mile

square millimeter

square meter

square kilometer

area of a rectangle

area of a rectangle
Let l be the length and w be the width of a rectangle. The Area (A) is:
A = [B]lw[/B]

Body Mass Index (BMI)

Solves for the popular health measurement of Body Mass Index or Weight using inches and pounds input or meters and kilos input.

Also calculates the estimated surface area of the body using the Mosteller Formula

Also calculates the estimated surface area of the body using the Mosteller Formula

Bretschneiders Formula

Calculates the area of a quadrilateral using Bretschneiders Formula

Cardioid

Shows you the area, arc length, polar equation of the horizontal cardioid, and the polar equation of the vertical cardioid

Circles

Calculates and solves for Radius, Diameter, Circumference, and Area of a Circle.

Cones

Calculates and solves for Radius, height, Volume (Capacity), Lateral Area, and Surface Area of a Cone.

Consider the formula for the area of a trapezoid: A=12h(a+b) . Is it mathematically simpler to solve

Consider the formula for the area of a trapezoid: A=12h(a+b) . Is it mathematically simpler to solve for a, b, or h? Why? Solve for each of these variables to demonstrate.
The variable "h" is the easiest to solve for. Because you only have one step. Let's review:
Divide each side of the equation by 12(a + b)
h = 12(a + b)/A
Solving for "a", we two steps. Divide each side by 12h:
A/12h = a + b
Subtract b from each side
a = A/12h - b
Solving for "b" takes two steps as well. Divide each side by 12h:
A/12h = a + b
Subtract a from each side
b = A/12h - a

Cube

Solves for Volume (Capacity), Lateral Area,Surface Area, and the value of a side for a cube.

Cuboid

Calculates the volume, surface area, diagonals, and space diagonal for a cuboid

Cylinders

Calculates and solves for Radius, Diameter, Volume (Capacity), Lateral Area, and Surface Area of a Cylinder.

Decagon

Solves for the side, perimeter, and area of a decagon.

Determine the area under the standard normal curve that lies between:

Determine the area under the standard normal curve that lies between:
(a) Z = -0.38 and Z = 0.38
(b) Z = -2.66 and Z = 0
(c) Z = -1.04 and Z - 1.67
[B](a) 0.2961 using our [URL='http://www.mathcelebrity.comzscore.php?z=+p%28-0.38%3Cz%3C0.38%29&pl=Calculate+Probability']z score calculator[/URL]
(b) 0.4961 using our [URL='http://www.mathcelebrity.com/zscore.php?z=+p%28-2.66%3Cz%3C0%29&pl=Calculate+Probability']z score calculator[/URL]
(c) 0.8034 using our [URL='http://www.mathcelebrity.com/zscore.php?z=+p%28-1.04%3Cz%3C1.67%29&pl=Calculate+Probability']z score calculator[/URL][/B]

Each side of a square is lengthened by 3 inches . The area of this new, larger square is 25 square

Each side of a square is lengthened by 3 inches . The area of this new, larger square is 25 square inches. Find the length of a side of the original square.
area of a square is s^2
New square has sides s + 3, so the area of 25 is:
(s + 3)^2 = 25
[URL='https://www.mathcelebrity.com/1unk.php?num=%28s%2B3%29%5E2%3D25&pl=Solve']Solving for s[/URL], we get:
s = [B]2[/B]

Equilateral Triangle

Given a side (a), this calculates the following items of the equilateral triangle:

* Perimeter (P)

* Semi-Perimeter (s)

* Area (A)

* altitudes (h_{a},h_{b},h_{c})

* medians (m_{a},m_{b},m_{c})

* angle bisectors (t_{a},t_{b},t_{c})

* Circumscribed Circle Radius (R)

* Inscribed Circle Radius (r)

* Perimeter (P)

* Semi-Perimeter (s)

* Area (A)

* altitudes (h

* medians (m

* angle bisectors (t

* Circumscribed Circle Radius (R)

* Inscribed Circle Radius (r)

Euclidean Geometry

Shows you the area, arc length, polar equation of the horizontal cardioid, and the polar equation of the vertical cardioid

Fantasia decided to paint her circular room which had a diameter of 25 feet. She started painting in

Fantasia decided to paint her circular room which had a diameter of 25 feet. She started painting in the center and when she had painted a circle with a 5-foot diameter, she used one quart of paint. How many more quarts of paint must Fantasia buy to finish her room?
The area formula for a circle is:
Area = pir^2
Area of full room
Radius = D/2
Radius = 25/2
Radius = 12.5
Area = 3.1415 * 12.5 * 12.5
Area = 490.625
Area of 5-foot diameter circle
Radius = D/2
Radius = 5/2
Radius = 2.5
Area = 3.1415 * 2.5 * 2.5
Area = 19.625
So 1 quart of paint covers 19.625 square feet
Area of unpainted room = Area of Room - Area of 5-foot diameter circle
Area of unpainted room = 490.625 - 19.625
Area of unpainted room = 471
Calculate quarts of paint needed:
Quarts of paint needed = Area of unpainted Room / square feet per quart of paint
Quarts of paint needed = 471/19.625
Quarts of paint needed = [B]24 quarts[/B]

Finding the dimensions

Expanded area = Original Area + area of Expansion
Area of Expansion = length expansion * width expansion

Hari planted 324 plants in such a way that there were as many rows of plants as there were number of

Hari planted 324 plants in such a way that there were as many rows of plants as there were number of columns. Find the number of rows and columns.
Let r be the number of rows and c be the number of columns. We have the area:
rc = 324
Since rows equal columns, we have a square, and we can set r = c.
c^2 = 324
Take the square root of each side:
[B]c = 18[/B]
Which means [B]r = 18[/B] as well.
What we have is a garden of 18 x 18.

heat loss of a glass window varies jointly as the window's area and the difference between the outsi

heat loss of a glass window varies jointly as the window's area and the difference between the outside and the inside temperature. a window 6 feet wide by 3 feet long loses 1,320 btu per hour when the temperature outside is 22 degree colder than the temperature inside.
Find the heat loss through a glass window that is 3 feet wide by 5 feet long when the temperature outside is 9 degree cooler than the temperature inside.
Find k of the equation:
6*3*22*k = 1320
396k = 1,320
k = 3.33333 [URL='https://www.mathcelebrity.com/1unk.php?num=396k%3D1320&pl=Solve']per our equation solver[/URL]
Now, find the heat loss for a 3x5 window when the temperature is 9 degrees cooler than the temperature inside:
3*5*9*3.333333 = [B]450 btu per hour[/B]

Help on problem

[B]List the answer being sought (words) ______Area of the garden
What is this answer related to the rectangle?_Have_________________________
List one piece of extraneous information____2m tall fence
List two formulas that will be needed_______P = 36. P = 2l + 2w
Write the equation for width_____________w = 2l - 6
Write the equation needed to solve this problem A = lw, P = 2l + 2w[/B]

Hemisphere

Calculates the base circumference, volume, curved surface area, base surface area, total surface area of a hemisphere with radius r

Heptagon

Solves for side length, perimeter, and area of a heptagon.

Hexagon

This calculator solves for side length (s), Area (A), and Perimeter (P) of a hexagon given one of the 3 entries.

If 800 feet of fencing is available, find the maximum area that can be enclosed.

If 800 feet of fencing is available, find the maximum area that can be enclosed.
Perimeter of a rectangle is:
2l + 2w = P
However, we're given one side (length) is bordered by the river and the fence length is 800, so we have:
So we have l + 2w = 800
Rearranging in terms of l, we have:
l = 800 - 2w
The Area of a rectangle is:
A = lw
Plug in the value for l in the perimeter into this:
A = (800 - 2w)w
A = 800w - 2w^2
Take the [URL='https://www.mathcelebrity.com/dfii.php?term1=800w+-+2w%5E2&fpt=0&ptarget1=0&ptarget2=0&itarget=0%2C1&starget=0%2C1&nsimp=8&pl=1st+Derivative']first derivative[/URL]:
A' = 800 - 4w
Now set this equal to 0 for maximum points:
4w = 800
[URL='https://www.mathcelebrity.com/1unk.php?num=4w%3D800&pl=Solve']Typing this equation into the search engine[/URL], we get:
w = 200
Now plug this into our perimeter equation:
l = 800 - 2(200)
l = 800 - 400
l = 400
The maximum area to be enclosed is;
A = lw
A = 400(200)
A = [B]80,000 square feet[/B]

If the circumference of a circular rug is 16? feet, then what is the area of the rug in terms of pi

If the circumference of a circular rug is 16? feet, then what is the area of the rug in terms of pi
C = 2pir, so we have:
C = 16?
16? = 2?r
Divide each side by 2?:
r = 16?/2?
r = 8
Now, the area of a circle A is denoted below:
A = ?r^2
Given r = 8 from above, we have:
A = ?(8)^2
A = [B]64?[/B]

Isosceles Triangle

Given a long side (a) and a short side (b), this determines the following items of the isosceles triangle:

* Area (A)

* Semi-Perimeter (s)

* Altitude a (ha)

* Altitude b (hb)

* Altitude c (hc)

* Area (A)

* Semi-Perimeter (s)

* Altitude a (ha)

* Altitude b (hb)

* Altitude c (hc)

Kamara has a square fence kennel area for her dogs in the backyard. The area of the kennel is 64 ft

Kamara has a square fence kennel area for her dogs in the backyard. The area of the kennel is 64 ft squared. What are the dimensions of the kennel? How many feet of fencing did she use? Explain.
Area of a square with side length (s) is:
A = s^2
Given A = 64, we have:
s^2 = 64
[URL='https://www.mathcelebrity.com/radex.php?num=sqrt(64%2F1)&pl=Simplify+Radical+Expression']Typing this equation into our math engine[/URL], we get:
s = 8
Which means the dimensions of the kennel are [B]8 x 8[/B].
How much fencing she used means perimeter. The perimeter P of a square with side length s is:
P = 4s
[URL='https://www.mathcelebrity.com/square.php?num=8&pl=Side&type=side&show_All=1']Given s = 8, we have[/URL]:
P = 4 * 8
P = [B]32[/B]

Keith is cutting two circular table tops out of a piece of plywood. the plywood is 4 feet by 8 feet

Keith is cutting two circular table tops out of a piece of plywood. the plywood is 4 feet by 8 feet and each table top has a diameter of 4 feet. If the price of a piece of plywood is $40, what is the value of the plywood that is wasted after the table tops are cut?
Area of the plywood = 4 * 8 = 32 square feet
[U]Calculate area of 1 round top[/U]
Diameter = 2
Radius = Diameter/2 = 4/2 = 2
Area of each round top = pir^2
Area of each round top = 3.14 * 2 * 2
Area of each round top = 12.56 square feet
[U]Calculate area of 2 round tops[/U]
Area of 2 round tops = 12.56 + 12.56
Area of 2 round tops = 25.12 sq feet
[U]Calculate wasted area:[/U]
Wasted area = area of the plywood - area of 2 round tops
Wasted area = 32 - 25.12
Wasted area = 6.88 sq feet
[U]Calculate cost per square foot of plywood:[/U]
Cost per sq foot of plywood = Price per plywood / area of the plywood
Cost per sq foot of plywood = 40/32
Cost per sq foot of plywood = $1.25
[U]Calculate the value of the plywood:[/U]
Value of the plywood = Wasted Area sq foot * Cost per sq foot of plywood
Value of the plywood = 6.88 * 1.25
Value of the plywood = [B]$8.60[/B]

Kites

This calculates perimeter and/or area of a kite given certain inputs such as short and long side, short and long diagonal, or angle between short and long side

Laura found a roll of fencing in her garage. She couldn't decide whether to fence in a square garden

Laura found a roll of fencing in her garage. She couldn't decide whether to fence in a square garden or a round garden with the fencing.
Laura did some calculations and found that a circular garden would give her 1380 more square feet than a square garden. How many feet of fencing were in the roll that Laura found? (Round to the nearest foot.)
Feet of fencing = n
Perimeter of square garden = n
Each side of square = n/4
Square garden's area = (n/4)^2 = n^2/16
Area of circle garden with circumference = n is:
Circumference = pi * d
n = pi * d
Divide body tissues by pi:
d = n/pi
Radius = n/2pi
Area = pi * n/2pi * n/2pi
Area = pin^2/4pi^2
Reduce by canceling pi:
n^2/4pi
n^2/4 * 3.14
n^2/12.56
The problem says that the difference between the square's area and the circle's area is equal to 1380 square feet.
Area of Circle - Area of Square = 1380
n^2/12.56 - n^2/16 = 1380
Common denominator = 200.96
(16n^2 - 12.56n^2)/200.96 = 1380
3.44n^2/200.96 = 1380
Cross multiply:
3.44n^2 = 277,324.8
n^2 = 80,617.7
n = 283.9
Nearest foot = [B]284[/B]

Marco orders a large pizza, with a diameter of 14 inches. It is cut into 8 congruent pieces. what is

Marco orders a large pizza, with a diameter of 14 inches. It is cut into 8 congruent pieces. what is the area of one piece?
A pizza is a circle. If the diameter of the pizza is 14 inches, the radius is 14/2 = 7 inches.
Area of a circle is pi(r^2). With r = 7, we have:
A =7^2(pi)
A = 49pi
Area of a slice of pizza is the area of the full pizza divided by 8
A(Slice) = [B]49pi/8[/B]

Math Written Assignment

Im sorta confused about this question?
He has decided to remove all the old sod (grass), bring in a new 4 inch layer of topsoil, install new in-ground sprinklers, and reseed the lawn. He seems to think that he'll be able to save money by hauling loads of topsoil from the store himself in his pickup truck, rather than paying for delivery, but I don't think he's right. You're going to help us settle this.
Here is (most of) the information you asked for:
[LIST]
[*]Is he redoing the whole yard or just the front?
He's redoing the whole yard
[*]How much topsoil does he need?
I'm not sure, you'll have to figure that out. Remember he's putting a new 4 inch layer down over all the area currently covered by grass in the overhead picture above.
[*]How big is the yard?
I'm not sure, but you can probably estimate it using the overhead picture.
[*]What kind of pickup truck does he drive?
A 2003 Ford F-150 XL.
[*]How much can the pickup carry?
The truck bed is 80 inches long, 69 inches wide, and 20 inches tall.
[*]How much is the delivery charge?
$30 per truckload on top of the soil cost. Each truckload can deliver up to 18 cubic yards.
[*]How much does the topsoil cost?
$18 per cubic yard (sold in 1/4 yard increments).
[*]How far is the soil store?
It is 9 miles away. It takes about 20 minutes to drive there.
[*]What gas mileage does the pickup truck get?
It averages 17 miles to the gallon.
[*]What is the current gas cost?
Assume it's $3.79/gallon.
[/LIST]
Using this information, figure out whether my neighbor will save money by picking up the soil himself. Use the results of your calculations to guide your decision: would you recommend that my neighbor pick up the soil himself, or pay for delivery?
Detail all your assumptions and calculations, and clearly write out your final conclusions.

Nine workers are hired to harvest potatoes from a field. Each is given a plot which is 5x5 feet in s

Nine workers are hired to harvest potatoes from a field. Each is given a plot which is 5x5 feet in size. What is the total area of the field?
Area of each plot is 5x5 = 25 square feet.
Total area = Area per plot * number of plots
Total area = 25 sq ft * 9
Total area = [B]225 sq ft[/B]

Nonagon

Calculates the side, perimeter, and area of a nonagon

Octagon

Calculate side, area, and perimeter of an octagon based on inputs

Pentagons

Given a side length and an apothem, this calculates the perimeter and area of the pentagon.

Pick's Theorem

This calculator determines the area of a simple polygon using interior points and boundary points using Pick's Theorem

Polygons

Using various input scenarios of a polygon such as side length, number of sides, apothem, and radius, this calculator determines Perimeter or a polygon and Area of the polygon.
This also determines interior angles of a polygon and diagonals of a polygon as well as the total number of 1 vertex diagonals.

Pyramids

Solves for Volume (Capacity), Surface Area, height, or radius of a Pyramid.

Quadrilateral

Given 4 points entered, this determines the area using Brahmaguptas Formula and perimeter of the quadrilateral formed by the points as well as checking to see if the quadrilateral (quadrangle) is a parallelogram.

Rectangle Word Problem

Solves word problems based on area or perimeter and variable side lengths

Rectangles and Parallelograms

Solve for Area, Perimeter, length, and width of a rectangle or parallelogram and also calculates the diagonal length as well as the circumradius and inradius.

Rectangular Solid

Solves for Volume (Capacity) of rectangular solid

Lateral Area of rectangular Solid

Surface Area of rectangular solid.

Lateral Area of rectangular Solid

Surface Area of rectangular solid.

Rhombus

Given inputs of a rhombus, this calculates the following:

Perimeter of a Rhombus

Area of a Rhombus

Side of a Rhombus

Perimeter of a Rhombus

Area of a Rhombus

Side of a Rhombus

Sheila wants build a rectangular play space for her dog. She has 100 feet of fencing and she wants i

Sheila wants build a rectangular play space for her dog. She has 100 feet of fencing and she wants it to be 5 times as long as it is wide. What dimensions should the play area be?
Sheila wants:
[LIST=1]
[*]l =5w
[*]2l + 2w = 100 <-- Perimeter
[/LIST]
Substitute (1) into (2)
2(5w) + 2w = 100
10w + 2w = 100
12w = 100
Divide each side by 12
[B]w = 8.3333[/B]
Which means l = 5(8.3333) -->[B] l = 41.6667[/B]

Spheres

Calculates and solves for Volume (Capacity), Surface Area, and Radius of a Sphere.

Squares

Solve for Area of a square, Perimeter of a square, side of a square, diagonal of a square.

Stress

Solves for any of the 3 items in the stress formula: Stress, Force, and Area

The area of a desert in Africa is 12 times the area of a desert in Asia. If the area of a desert in

The area of a desert in Africa is 12 times the area of a desert in Asia. If the area of a desert in Asia is Y square miles, express the area of a desert in Africa as an algebraic expression in Y.
[B]Africa Area = 12Y[/B]

The base of a triangle with a height of 7 units is represented by the formula b=2/7A. The base of th

The base of a triangle with a height of 7 units is represented by the formula b=2/7A. The base of the triangle is less than 10 units. Write and solve an inequality that represents the possible area A of the triangle
We're given:
b=2/7A
We're also told that b is less than 10. So we have:
2/7A < 10
2A/7 < 10
Cross multiply:
2A < 7 * 10
2A < 70
Divide each side of the inequality by 2 to isolate A
2A/2 < 70/2
Cancel the 2's on the left side and we get:
A < [B]35[/B]

The dimensions of a rectangle are 30 cm and 18 cm. When its length decreased by x cm and its width i

The dimensions of a rectangle are 30 cm and 18 cm. When its length decreased
by x cm and its width is increased by x cm, its area is increased by 35 sq. cm.
a. Express the new length and the new width in terms of x.
b. Express the new area of the rectangle in terms of x.
c. Find the value of x.
Calculate the current area. Using our [URL='https://www.mathcelebrity.com/rectangle.php?l=30&w=18&a=&p=&pl=Calculate+Rectangle']rectangle calculator with length = 30 and width = 18[/URL], we get:
A = 540
a) Decrease length by x and increase width by x, and we get:
[LIST]
[*]length = [B]30 - x[/B]
[*]width = [B]18 + x[/B]
[/LIST]
b) Our new area using the lw = A formula is:
(30 - x)(18 + x) = 540 + 35
Multiplying through and simplifying, we get:
540 - 18x + 30x - x^2 = 575
[B]-x^2 + 12x + 540 = 575[/B]
c) We have a quadratic equation. To solve this, [URL='https://www.mathcelebrity.com/quadratic.php?num=-x%5E2%2B12x%2B540%3D575&pl=Solve+Quadratic+Equation&hintnum=+0']we type it in our search engine, choose solve[/URL], and we get:
[B]x = 5 or x = 7[/B]
Trying x = 5, we get:
A = (30 - 5)(18 + 5)
A = 25 * 23
A = 575
Now let's try x = 7:
A = (30 - 7)(18 + 7)
A = 23 * 25
A = 575
They both check out.
So we can have

The length of a wooden frame is 1 foot longer than its width and its area is equal to 12ft²

The length of a wooden frame is 1 foot longer than its width and its area is equal to 12ft²
The frame is a rectangle. The area of a rectangle is A = lw. So were given:
[LIST=1]
[*]l = w + 1
[*]lw = 12
[/LIST]
Substitute equation (1) into equation (2) for l:
(w + 1) * w = 12
Multiply through and simplify:
w^2 + w = 12
We have a quadratic equation. To solve for w, we type this equation into our search engine and we get two solutions:
w = 3
w = -4
Since width cannot be negative, we choose the positive result and have:
w = [B]3[/B]
To solve for length, we plug w = 3 into equation (1) above and get:
l = 3 + 1
l = [B]4[/B]

The moon's diameter is 2,159 miles. What is the surface area of the moon? Round to the nearest mile.

The moon's diameter is 2,159 miles. What is the surface area of the moon? Round to the nearest mile.
The moon is a sphere. So our Surface Area formula is:
S =4pir^2
If diameter is 2,159, then radius is 2,159/2 = 1079.5. Plug this into the Surface Area of a sphere formula:
S = 4 * pi * 1079.5^2
S = 4 * pi *1165320.25
S = 4661281 pi
S = [B]14,643,846.15 square miles[/B]

The perpendicular height of a right-angled triangle is 70 mm longer than the base. Find the perimete

The perpendicular height of a right-angled triangle is 70 mm longer than the base. Find the perimeter of the triangle if its area is 3000.
[LIST]
[*]h = b + 70
[*]A = 1/2bh = 3000
[/LIST]
Substitute the height equation into the area equation
1/2b(b + 70) = 3000
Multiply each side by 2
b^2 + 70b = 6000
Subtract 6000 from each side:
b^2 + 70b - 6000 = 0
Using our [URL='http://www.mathcelebrity.com/quadratic.php?num=b%5E2%2B70b-6000%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic calculator[/URL], we get:
b = 50 and b = -120
Since the base cannot be negative, we use b = 50.
If b = 50, then h = 50 + 70 = 120
The perimeter is b + h + hypotenuse
Using the [URL='http://www.mathcelebrity.com/righttriangle.php?angle_a=&a=70&angle_b=&b=50&c=&pl=Calculate+Right+Triangle']right-triangle calculator[/URL], we get hypotenuse = 86.02
Adding up all 3 for the perimeter: 50 + 70 + 86.02 = [B]206.02[/B]

The width of a rectangle is fixed at 4cm. For what lengths will the area be less than 86 cm^2

The width of a rectangle is fixed at 4cm. For what lengths will the area be less than 86 cm^2
The Area (A) of a rectangle is given by:
A = lw
With an area of [I]less than[/I] 86 and a width of 4, we have the following inequality:
4l < 86
To solve for l, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=4l%3C86&pl=Show+Interval+Notation']type this inequality into our search engine[/URL] and we get:
[B]l < 21.5[/B]

Torus

Calculates the volume of a torus and surface area of a torus given major radius and minor radius.

Trapezoids

This calculator determines the following items for a trapezoid based on given inputs:

* Area of trapezoid

* Perimeter of a Trapezoid

* Area of trapezoid

* Perimeter of a Trapezoid

Triangle Coordinate Items

Enter 3 points for the vertices of a triangle, and this will calculate the area of that triangle and the centroid.

Triangle Solver and Classify Triangles

Solves a triangle including area using the following solving methods

Side-Angle-Side (SAS) Side Angle Side

Angle-Side-Angle (ASA) Angle Side Angle

Side-Side-Angle (SSA) Side Angle Side

Side-Side-Side (SSS) Side Side Side

Area (A) is solved using Herons Formula

Law of Sines

Law of Cosines

Also classifies triangles based on sides and angles entered.

Side-Angle-Side (SAS) Side Angle Side

Angle-Side-Angle (ASA) Angle Side Angle

Side-Side-Angle (SSA) Side Angle Side

Side-Side-Side (SSS) Side Side Side

Area (A) is solved using Herons Formula

Law of Sines

Law of Cosines

Also classifies triangles based on sides and angles entered.

Use the definite integral to find the area between the x-axis and the function f(x)= x^2-x-12 over t

Use the definite integral to find the area between the x-axis and the function f(x)= x^2-x-12 over the interval [ -5, 10].
Using our [URL='http://www.mathcelebrity.com/dfii.php?term1=x%5E2-x-12&fpt=0&ptarget1=0&ptarget2=0&itarget=-5%2C10&starget=0%2C1&nsimp=8&pl=Integral']integral calculator[/URL], we get:
[B]157.5[/B]

What is the area of a triangular parking lot with a width of 200m and a length of 100m?What is the a

What is the area of a triangular parking lot with a width of 200m and a length of 100m?
Area of a Triangle = bh/2
Plugging in our numbers, we get:
Area of Parking Lot = 200(100)/2
Area of Parking Lot = 100 * 100
Area of Parking Lot = [B]10,000 sq meters[/B]

When the side of a square is doubled in length, its area increases by 432 square inches. What is the

When the side of a square is doubled in length, its area increases by 432 square inches. What is the size of the original square?
Original square side length is s
Area = s^2
Double the side lengths to 2s
New area = (2s)^2 = 4s^2
Setup the difference relation:
4s^2 - s^2 = 432
3s^2 = 432
Divide each side by 3:
3s^2/3 = 432/3
s^2 = 144
s = [B]12[/B]

Which of the following is NOT TRUE about the distribution for averages?

Which of the following is NOT TRUE about the distribution for averages?
a. The mean, median, and mode are equal.
b. The area under the curve is one.
c. The curve never touches the x-axis.
d. The curve is skewed to the right.
Answer is d, the curve is skewed to the right
For a normal distribution:
[LIST]
[*] The area under the curve for a standard normal distribution equals 1
[*] Mean media mode are equal
[*] Never touches the x-axis since in theory, all events have some probability of occuring
[/LIST]