What is the area of a 7 sided polygon with an apothem of 2.5 and s radius of 2.77?
A regular 7-sided polygon can be thought of as being made of 7 isosceles triangles. Each triangle has an apex angle theta = 2pi/7. The height is h = 2.5 and half the base length is b = h*tan(theta/2). Hence the overall area of the polygon is:
A = 7*b*h or A = 7*2.5*tan(pi/7)*2.5 or A ≈ 21.07