1
Question
Find the area of an equilateral triangle whose perimeter is 12 cm.
Find the area of an equilateral triangle whose perimeter is 12 cm.
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Solution
The correct option is C 6.92 sq. cm
We 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
We 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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