An equilateral triangle has a side of length 12 inches. What is the area of the triangle, in square inches? Express your answer in simplest radical form.

Guest Feb 27, 2020

#3**+2 **

*An equilateral triangle has a side of length 12 inches. What is the area of the triangle, in square inches? Express your answer in simplest radical form.*

Area of a triangle is one-half the base times the height. The base of this triangle is 12 inches of course. What is the height?

The height would be the length of the line dropped perpendicular from the top vertex to the base. This forms a right triangle, with one side of 6 inches (half the base side, 6 inches) and the hypotenuse (12 inches). We use Pythagoras' Theorem to determine the other side.

a^{2} + b^{2} = c^{2}

6^{2} + b^{2} = 12^{2}

36 + b^{2} = 144

b^{2} = 144 – 36 = 108

b = sqrt(108) = sqrt(36•3) = 6•sqrt(3) This is the height.

The area of a triangle is (1/2) • base • height

A = (1/2) • (12) • (6 • sqrt(3))

**A = 36 • sqrt(3)**

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Guest Feb 27, 2020