A regular hexagon has sides 2 feet long. What is the exact area of the hexagon? What is the approximate area of the hexagon?
1 answer:
The formula for the area of a hexagon is
![A=\frac{3\sqrt[]{3}}{2}s^2](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B3%5Csqrt%5B%5D%7B3%7D%7D%7B2%7Ds%5E2)
where 's' is the length of one side of the regular hexagon.
The side of our regular hexagon is 2 feet, therefore, its area is
![\begin{gathered} A=\frac{3\sqrt[]{3}}{2}\cdot(2)^2=6\sqrt[]{3} \\ 6\sqrt[]{3}=10.3923048454\ldots\approx10 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20A%3D%5Cfrac%7B3%5Csqrt%5B%5D%7B3%7D%7D%7B2%7D%5Ccdot%282%29%5E2%3D6%5Csqrt%5B%5D%7B3%7D%20%5C%5C%206%5Csqrt%5B%5D%7B3%7D%3D10.3923048454%5Cldots%5Capprox10%20%5Cend%7Bgathered%7D)
The exact area of the hexagon is 6√3 ft², which is approximately 10 ft².
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