Divide the polygon into triangles and using trig, solve for the area.
1. A regular heptagon with a side of 7 inches. (The answer is 178.06 sq in, I just need to know how to solve this using trig.)
2. A square with a side of 2 feet (answer is 4 sq. ft)
If you take the center of a regular n-polygon and you connect it with all the vertices, you will get n isosceles triangles with the angle between two equal sides equal to and the opposite side equal to the side of a polygon. Thus, you can solve this triangle to get that the equal sides of this triangle are , where a is the polygon side (we appply simply the law of cosines to the side a). Thus the area of one triangle is , and so the whole area is . Applying this formula we get :
Comments