Question 324408
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Using the properties of a 30-60-90 right triangle, you can readily determine that the measure of the apothem and the radius of the circumcircle (which is equal to the measure of a side of a regular hexagon) are in proportion:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 1:\frac{2\sqrt{3}}{3}]


Hence a regular hexagon with an apothem of *[tex \LARGE 8\sqrt{3}] has a side that measures *[tex \LARGE 16].


The perimeter of such a hexagon is simply 6 times the measure of a side, and therefore half of the perimeter is 3 times the measure of a side.


The area of a hexagon with perimeter *[tex \LARGE P] and apothem *[tex \LARGE a] is given by:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ A\ =\ \frac{Pa}{2}]



John
*[tex \LARGE e^{i\pi} + 1 = 0]
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