HELP

144 inches

72 inch

an equalatral tryangle has all the same side length, so (12 x 12) / 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. 

a² + b² = c² 

6² + b² = 12² 

36 + b² = 144 

b² = 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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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.

a = 12 in

h = sqrt(3) * a/2 = 10.39230485

Δ Area = h * a/2 ≈ 62.354 in²  

The way you solve for an equalateral triangle is (s^2 * sqrt(3)) / 4 

Side is 12

144 * sqrt(3) divided by 4 which is 36 sqrt(3)