Question

Find the area of regular pentagon whose each side measures 5 cm and the radius of circumscribed circle is 3.5 cm.

Answer 1

Side (a) of the regular pentagon = 5 cm
Radius (R) of the circumscribed circle = 3.5 cm
Number of sides (n) = 5
∴ Area of the regular polygon = $\frac{1}{2}\times n\times a\times \sqrt{R^2-\frac{a^2}{4}}$
$$\begin{gathered} =\frac{1}{2}\times 5\times 5\times \sqrt{3.5^2-{\displaystyle \frac{5^2}{4}}} \\ =12.5\times \sqrt{12.25-\frac{25}{4}} \\ =12.5\times \sqrt{12.25-6.25} \\ =12.5\sqrt{6} \\ =30.625{\mathrm{cm}}^2(\sqrt{6}=2.45) \end{gathered}$$