What is the area of an equilateral triangle with height of 9 inches?

1 Answer

A=27346.77 inches.

Explanation:

In such situations, the first step is to draw a picture.

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In relation to the notation introduced by the picture, we know that h=9 inches.

Knowing that the triangle is equilateral makes everything easier: the heights are also medians. So the height h is perpendicular to the side AB and it divides it in two halves, which are a2 long.

Then, the triangle is divided into two congruent right triangles and the Pythagorean Theorem holds for one of these two right triangles: a2=h2+(a2)2. So 34a2=h2 i.e. a2=43h2. In the end, we get that the side is given by a=233h=2339=6310.39 inches.

Now the area:
A=ah2=233hh2=33h2=3381=27346.77 inches.