Find the area of a regular polygon having 15 sides which is inscribed in a circle of radius 4cm. (sin 24 = 0.407)

Solution. 

The central angle made by the side of a regular polygon of 15 sides inscribed in a circle = (3600 ÷ 15) = 240

In the figure AB is one of the sides of the regular polygon.
∆ OAB is one of the 15 congruent triangles made by the regular polygon.
Radius of the circle (r) = OA = 4 cm




The area of the regular polygon of 15 sides is 48.84 cm2