1. ## Area of hexagon

A regular hexagon is inscribed in a circle with radius 11. Find the area of the hexagon.

Any help is appreciated!

2. Hello, live_laugh_luv27!

A regular hexagon is inscribed in a circle with radius 11.
Find the area of the hexagon.
Make a sketch.
We find that the hexagon is made up of six equilateral triangles of side 11.

The area of an equilateral triangle of side $\displaystyle x$ is: .$\displaystyle A \:=\:\tfrac{\sqrt{3}}{4}x^2$

With side 11, the area is: .$\displaystyle \tfrac{\sqrt{3}}{4}(11^2) \:=\:\tfrac{121\sqrt{3}}{4}$

The area of the hexagon is: .$\displaystyle 6 \times\tfrac{121\sqrt{3}}{4} \;=\;\frac{363\sqrt{3}}{2}$

3. Originally Posted by Soroban
Hello, live_laugh_luv27!

Make a sketch.
We find that the hexagon is made up of six equilateral triangles of side 11.

The area of an equilateral triangle of side $\displaystyle x$ is: .$\displaystyle A \:=\:\tfrac{\sqrt{3}}{4}x^2$

With side 11, the area is: .$\displaystyle \tfrac{\sqrt{3}}{4}(11^2) \:=\:\tfrac{121\sqrt{3}}{4}$

The area of the hexagon is: .$\displaystyle 6 \times\tfrac{121\sqrt{3}}{4} \;=\;\frac{363\sqrt{3}}{2}$
Thanks for taking the time to explain that to me..I really appreciate your help