The Area Of The Pentagon
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 *
Area of pentagon = 5 * area of each triangle.