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

Question 276192: Find the area of an equilateral triangle, with apothem 10 times the square root of 3. inches?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

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

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