Pythagorean Theroem - For Right Triangles

a + b = c

2          2         2

b

c

a

Heron's Formula - For All Triangles

If s = (a + b + c) / 2

Area = √ s  (s - a) (s - b) (s - c)

If s = (a + b + c) / 2

Area = √ s  (s - a) (s - b) (s - c)

c

a

In this example, each side of the hexagon is 2 units long. The distance from the center to the middle of the side is √3 . So the perimeter is 12 and half of it is 6. 6 * √3 = 6√3 .

The area of a regular polygon is half of its perimeter multiplied by the distance from the center to the middle of a side.

 

The sum of a polygon with n sides is (n - 2)(180).