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What is the area of an equilateral triangle if the side length is 12 cm?

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gbaby123 | Student, Grade 10 | eNotes Newbie

Posted May 11, 2010 at 9:16 AM via web

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What is the area of an equilateral triangle if the side length is 12 cm?

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pohnpei397 | College Teacher | (Level 3) Distinguished Educator

Posted May 11, 2010 at 9:25 AM (Answer #1)

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You need to know two things to solve this.  First, you have to remember that the area of a triangle is .5(base*height).  Second, you have to know the Pythagorean Theorem.

Because we know that the legs are each 12 inches, we know that the base is 12 inches.  So now we need to know the height.

We know that one leg is 6 inches (half of 12) and the hypotenuse is 12 inches.  So 6^2+x^2 = 12^2

36 + x^2 = 144

x^2 = 108

So the height is the square root of 108.

Now to get the area you take.5 (12*square root of 108).

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krishna-agrawala | College Teacher | Valedictorian

Posted May 11, 2010 at 4:21 PM (Answer #2)

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The area of an equilateral triangle is given by the formula:

A = [3^(1/2)]*[(L^2)/4]

Where:

A = area

L = Length of the sides of the triangle.

It is given:

L = 12 cm.

Substituting this value of L in equation of area we get:

A = [3^(1/2)]*[(12^2)/4]

= [3^(1/2)]*(144/4) = 1.73205*36 = 62.3538 cm^2

Answer:

Area of triangle = 62.3538 cm^2

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