The Area Of The Pentagon

Figure 1

The area of the pentagon is the combined area of the 5 triangles shown in
Figure 1, each of which has a vertex at O.

What is the area of each of these triangles?

Lets work with triangle ODE.

From Pentagon Construction
we know that the distance O to any vertex is

In order to get the area of a triangle we need to know OF.

DE = side of pentagon = s, so FE =

height of triangle = OF² = OE² - FE² = =

Now we can get the area of each triangle, for the area = 1/2 * base *
height:

Area of pentagon = 5 * area of each triangle.