SOLUTION: Find the area of an equilateral triangle, with apothem 10 times the square root of 3. inches?

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Question 276192: Find the area of an equilateral triangle, with apothem 10 times the square root of 3. inches?
Answer by solver91311(24713) About Me  (Show Source):
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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 .

is 20 times greater than , 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:



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



John