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Answer

↓Steps Explained:↓

Hexagon has Area (A) of of 10

calculate the side length (s) and Perimeter (P)

Calculate side length (s):

The formula for Area of a Hexagon is given below:

A  =	3√3s2
	2

Multiply each side by 2:

2A = 3√3s²

Divide each side by 3√3:

2A
3√3

=

3√3s2

3√3

Cancel the right side numbers, we get:

s2  =	2A
	3√3

Plugging in our A = 10, we get:

s2  =	2(10)
	3√3

s2  =	20
	3√3

s² = 3.8490017945975

s = √3.8490017945975

s = 1.9618873042551

Calculate Perimeter:

P = 6 x s

P = 6 x 1.9618873042551

P = 11.771323825531

Calculate Sum of the Interior Angles:

Interior Angle Sum = (sides - 2) x 180°

Interior Angle Sum = (6 - 2) x 180°

Interior Angle Sum = 4 x 180°

Interior Angle sum = 720°

Calculate polygon diagonals

Diagonals  =	n(n - 3)
	2

Diagonals  =	6(6 - 3)
	2

Diagonals  =	6(3)
	2

Diagonals  =	18
	2

Diagonals = 9

Calculate 1 vertex diagonals:

1 vertex Diagonals = n - 3

1 vertex Diagonals = 6 - 3

1 vertex Diagonals = 3

Calculate triangles from one vertex:

Triangles = N - 2

Triangles = 6 - 2

Triangles = 4

Other Properties:

Sides (Edges) = 6

Faces = 1

Vertices = 6

Final Answers

A = 10
s = 1.9618873042551
P = 11.771323825531
Interior Angle sum = 720°
Diagonals = 9
1 vertex Diagonals = 3
Triangles = 4
Sides (Edges) = 6
Faces = 1
Vertices = 6

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