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# HELP

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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.

Feb 27, 2020

#1
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144 inches

Feb 27, 2020
#2
+383
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72 inch

an equalatral tryangle has all the same side length, so (12 x 12) / 2

Feb 27, 2020
edited by TacoBell  Feb 27, 2020
#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.

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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Feb 27, 2020
#4
+1440
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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

Feb 27, 2020
#6
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Dragan, your answer is mathematically correct, but the problem specified to put the answer in simplest radical form.  Apparently you don't know what that means, so I recommend that you look it up with google for a full explanation.

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Guest Feb 29, 2020
#5
+110
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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)

Feb 28, 2020