Question 276192
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The apothem of an equilateral triangle divides the triangle into two 30-60-90 right triangles, where the apothem is the long leg of the triangle.


The sides of a 30-60-90 right triangle are in proportion *[tex \LARGE \frac{1}{2}:\frac{\sqrt{3}}{2}:1].


*[tex \LARGE 10\sqrt{3}] is 20 times greater than *[tex \LARGE \frac{\sqrt{3}}{2}], therefore the other two sides must measure 10 and 20 inches.


The area of a right triangle is one-half of the product of the measures of the two legs.  For your problem:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{10\,\cdot\,10\sqrt{3}}{2}]


But that is the area of only one-half of the equilateral triangle, so the total area you seek is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 10\,\cdot\,10\sqrt{3}\ =\ 100\sqrt{3}]


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