Chapter E, Problem 11.9EX

To determine

To find the area of a regular hexagon inscribed in a circle.

Answer to Problem 11.9EX

Option (b)

Explanation of Solution

Given information: Regular hexagon inscribed in a circle with radius 8.

Concept used:

  $\text{Area}\text{of}\text{equilateral}\text{triangle}=\frac{\sqrt{3}}{4}\times a^2$

Regular hexagon composed of 6 equilateral triangle. Therefore, the area of regular hexagon is equal to the area of 6 equilateral triangles.

  $\text{Area}\text{of}\text{regular}\text{hexagon}=6\times \frac{\sqrt{3}}{4}\times a^2=6\times \frac{\sqrt{3}}{4}\times 8\times 8=96\sqrt{3}$

Hence, the area of the regular hexagon is $96\sqrt{3}$ units .