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Polygons Calculator

Enter 2 values

<-- Side Length
<-- # of Sides
<-- Radius
<-- Apothem
<-- Perimeter
  
You entered decagon
This corresponds to an 10 sided polygon

Calculate Sum of the Interior Angles:

Interior Angle Sum = (n - 2) x 180°
Interior Angle Sum = (10 - 2) x 180°
Interior Angle Sum = (8) x 180°
Interior Angle Sum = 1440°

Calculate the number of diagonals

Diagonals  =  n(n - 3)
  2

Diagonals  =  10(10 - 3)
  2

Diagonals  =  10(7)
  2

Diagonals  =  70
  2

Diagonals = 35

Calculate 1 vertex diagonals

1 vertex Diagonals = n - 3
1 vertex Diagonals = 10 - 3
1 vertex Diagonals = 7

Calculate 1 vertex triangles

Triangles = N - 2
Triangles = 10 - 2
Triangles = 8

Determine polygon type

Since the polygon has 10 sides, it is a decagon

Final Answers




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What is the Answer?

Interior Angle Sum = 1440
Diagonals = 35
1 Vertex Diagonals = 7
Triangles = 8
Polygon Type = decagon

How does the Polygons Calculator work?

Free Polygons Calculator - 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.
This calculator has 5 inputs.

What 13 formulas are used for the Polygons Calculator?

P = n x s
A = s2n/4tan(π/n)
Interior Angle Sum = (n - 2) x 180°
Diagonals = n(n - 3)/2
1 vertex Diagonals = n - 3
Triangles = N - 2
5 sides = Pentagon
6 sides = Hexagon
7 sides = Heptagon
8 sides = Octagon
9 sides = Nonagon
10 sides = Decagon


For more math formulas, check out our Formula Dossier

What 6 concepts are covered in the Polygons Calculator?

apothem
a line segment from the center to the midpoint of one of its sides
area
Number of square units covering the shape
diagonal
line segment that goes from one corner to another, but is not an edge
perimeter
The distance around a shape or object
polygon
A plane figure bounded by a set of straight lines
radius
Distance from the center of a circle to the edge
C/2π

Example calculations for the Polygons Calculator

  1. diagonals for polygon with 10 sides
  2. interior angle with 7 sided polygon
  3. vertex for polygon with 5 sides

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