Chapter 11.5, Problem 11PSA

To determine

To Calculate: The area of regular hexagon.

Answer to Problem 11PSA

The area of regular hexagon is $216\sqrt{3}$

Explanation of Solution

Given information:

Radius of the circle is,“ r ”= $12$

Formula used:

Here, we are using the formula

Area of equilateral triangle = $\frac{\sqrt{3}}{4}{a}^2$ ( here, “ a ” is side)

Calculation: Here, a = r = $12$ (given)

  → $\frac{\sqrt{3}}{4}\times 12\times 12$

  → $36\sqrt{3}$

Now, for six triangles

  → $36\sqrt{3}\times 6=216\sqrt{3}$

Conclusion: Hence,the area of regular hexagon is $216\sqrt{3}$