A regular hexagon is inscribed in a circle with radius 11. Find the area of the hexagon.
Any help is appreciated!
Hello, live_laugh_luv27!
Make a sketch.A regular hexagon is inscribed in a circle with radius 11.
Find the area of the hexagon.
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: .$\displaystyle 6 \times\tfrac{121\sqrt{3}}{4} \;=\;\frac{363\sqrt{3}}{2}$