Area of hexagon

**live_laugh_luv27** · May 4th 2009, 05:44 PM

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

Any help is appreciated!

**Soroban** · May 4th 2009, 06:55 PM

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 $x$ is: . $A \:=\:\tfrac{\sqrt{3}}{4}x^2$

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

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

**live_laugh_luv27** · May 4th 2009, 07:01 PM

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 $x$ is: . $A \:=\:\tfrac{\sqrt{3}}{4}x^2$

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

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

Thanks for taking the time to explain that to me..I really appreciate your help

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