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Question

# Find the area of an equilateral triangle whose perimeter is 12 cm.

A
3.46 sq. cm
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B
5.19 sq. cm
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C
6.92 sq. cm
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D
8.65 sq. cm
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Solution

## The correct option is C 6.92 sq. cmWe know, the perimeter of a triangle is equal to the sum of all the sides. Therefore, Perimeter = a+a+a = 12 cm a = 4 cm Since we don't know the height, let us split the equilateral triangle into 2 triangles, by drawing a perpendicular to the base. So, we get two triangles with base 4/2 cm each, and let the height be ‘h’. Using pythagoras theorem, h = √(16-4) h = 2√3 cm So, the area of an equilateral triangle, A = 1/2×base×height = 1/2×4×2√3 = 4√3 sq. cm

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