SOLUTION: find the area of an equilateral triangle with an apothem having a length of 4 feet. round to the nearest tenth
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Question 310745: find the area of an equilateral triangle with an apothem having a length of 4 feet. round to the nearest tenth
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The apothem of an equilateral triangle forms a 30-60-90 right triangle where the apothem is the long leg, one side of the triangle is the hypotenuse, and one-half of the side is the short leg.
With a tip o'the hat to Mr. Pythagoras, letting 
represent the measure of the hypotenuse, we can say:
^2\ +\ 16)
And a little algebra and rationalizing the denominator gets us to:
Hence the measure of the short side of the triangle is:
The 30-60-90 triangle is one-half of the equilateral triangle, so:
\ =\ \frac{4\,\cdot\,4\sqrt{3}}{3}\ =\ \frac{16\sqrt{3}}{3}\ \approx\ 9.2)
feet.
John
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