Answer-The altitude of an equilateral triangle is 6√3 cm. Find the area of the equilateral triangle.

Q: Answer-The altitude of an equilateral triangle is 6√3 cm. Find the area of the equilateral triangle.

Let each side of the equilateral triangle be a cmTherefore, a 2 a 2 4 63 2 Or, 3a 2 4 108Or, a 2 144Or, a 12 cmTherefore, area of the equilateral triangle 3a 2 4Or, area of the equilateral triangle 3 1444 363 cm 2

Question

Accepted Answer

Let each side of the equilateral triangle be ‘a’ cm

Therefore, (a ² – a ² /4) = (6√3) ²

Or, 3a ² /4 = 108

Or, a ² = 144

Or, a = 12 cm

Therefore, area of the equilateral triangle = √3a ² /4

Or, area of the equilateral triangle = (√3 × 144)/4 = 36√3 cm ²

The altitude of an equilateral triangle is 6√3 cm.

Solution