SOLUTION: Find the area of an equilateral triangle that has a perimeter of 21 inches. Round the answer to one decimal place.

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Question 363105: Find the area of an equilateral triangle that has a perimeter of 21 inches. Round the answer to one decimal place.
Answer by CharlesG2(834) (Show Source):
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Find the area of an equilateral triangle that has a perimeter of 21 inches. Round the answer to one decimal place.

area A of a triangle = 1/2 * base b * height h
P perimeter triangle = 21 inches
length of one side of equilateral triangle = 21/3 = 7 inches
an equilateral triangle is made up of 2 right triangles
in this case each has a base of 7/2 = 3.5 inches,
and each has an hypotenuse of 7 inches
find the height using Pythagorean Theorem
(7/2)^2 + h^2 = 7^2
49/4 + h^2 = 49
49/4 + h^2 = 196/4
h^2 = 147/4 = (49 * 3)/4
h = (7sqrt(3))/2 inches
area A = 1/2 * 7 * (7sqrt(3))/2
A = (49sqrt(3))/4 = 21.2 square inches rounded to nearest tenth