Question

A regular polygon of side 15 cm is inscribed in a circle of radius 4 cm. Find the area of
the polygon. (sin 24° = 0.407)​

Answer 1

$\Large\underline{\underline{\mathfrak \red{Solution:}}}$

$\large\underline{\underline{\sf Given:}}$

• Regular polygon side = 15cm
• Radius of circle = 4cm

$\large\underline{\underline{\sf To\:Find:}}$

• Area of Polygon (A).

The central angle made by the side of a regular polygon of 15 sides inscribed in a circle = (360° ÷ 15) = 240°

∆ OAB is one of the 15 congruent triangles made by the regular polygon.

$\implies{\sf Radius\:of \:the \:circle \:(r) = OA = 4 cm}$

$\implies{\sf \triangle A(OAB)=\dfrac{1}{2}×r^2sin\theta }$

$\implies{\sf \dfrac{1}{2}×4^2×0.407}$

$\implies{\sf \dfrac{1}{2}×16×0.407 }$

$\implies{\sf 8×0.407}$

$\implies{\sf 3.256\:cm^2}$

$\implies{\sf A=regular\:polygon\:of\:15\:sides }$

$\implies{\sf A(OAB)×15 }$

$\implies{\sf 3.256×15 }$

$\implies{\sf 48.84\:cm^2}$

$\Large\underline{\underline{\mathfrak \red{Answer:}}}$

${\sf \therefore \:area\:of\:polygon\:is\:48.84\:cm^2}$