SOLUTION: 37) Find the area of an equilateral triangle with apothem 9.

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Question 973425: 37) Find the area of an equilateral triangle with apothem 9.
Answer by macston(5194) About Me  (Show Source):
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s=side of equilateral triangle, a=apothem=9
The apothem is the longer leg of a 30-60-90 triangle
with one side of the equilateral triangle as hypotenuse
and one half one side as the shorter leg.
s%5E2=%28s%2F2%29%5E2%2Ba%5E2
s%5E2=%28s%5E2%2F4%29%2B9%5E2
s%5E2=s%5E2%2F4%2B81 Multiply by 4
4s%5E2=s%5E2%2B324
3s%5E2=324
s%5E2=108
s=10.39
The side of the equilateral triangle is 10.39.
The base of the right triangle which makes up half of the
equilateral triangle is 1/2 of a side (1/2)(10.39)=5.195 units
The height of this right triangle is the apothem (9 units)
The area of the right triangle is (1/2)(5.195)(9)=23.4 square units
Since two of these right triangles make up the equilateral triangle,
area of the equilateral triangle is (2)(23.4)=46.8 square units.