> Find the area of a regular pentagon with an apothem of 8cm?

Find the area of a regular pentagon with an apothem of 8cm?

Posted at: 2014-06-09 
please explain!!
Divide pentagon into 5 isosceles triangles. Each triangle has vertex angle = 360/5 = 72 h = altitude of triangle = 8 b = base of triangle tan(72/2) = (b/2)/h b = 2h tan(36) b = 16 tan(36) Each triangle has area = 1/2 * 8 * 16 tan(36) = 64 tan(36) Area of pentagon = 5 * 64 tan(36) = 320 tan(36) = 232.4936