Question

A regular hexagon is inscribed in a circle of radius $10$ cm. The area of the hexagon is :

• A. $150\sqrt{3}$sq. cm.
• B. $150$ sq. cm.
• C. $25\sqrt{3}$ sq. cm.
• D. $600$ sq. cm.
• E. $300\sqrt{3}$ sq. cm.

Answer 1

The correct option is A $150\sqrt{3}$sq. cm.

Given radius $=10cm$ $\Rightarrow$side $=10cm$ as triangle formed here is an equilateral trinagle.

$\therefore area=6\times \frac{\sqrt{3}}{4}{a}^2$

$\Rightarrow area=\frac{3\sqrt{3}}{2}\times {10}^2$

$\therefore area=150\sqrt{3}$