Question

Find the area of 9-sided regular polygon whose each side measures 6 cm and the radius of circumscribed circle is 4 cm.

Answer 1

Side (a) of the given regular polygon = 6 cm
Radius (R) of the circumscribed circle = 4 cm
Number of sides (n) = 9
∴ Area of the polygon = $\frac{1}{2}\times n\times a\times \sqrt{R^2-\frac{a^2}{4}}$
$$\begin{gathered} =\frac{1}{2}\times 9\times 6\times \sqrt{4^2-\frac{6^2}{4}} \\ =27\times \sqrt{16-\frac{36}{4}} \\ =27\times \sqrt{16-9} \\ =27\sqrt{7}{\mathrm{cm}}^2 \end{gathered}$$