If the altitude of an equilateral triangle is 4√3 cm, then find the area of an equilateral triangle.
1. 16√3
2. 8√3
3. 64√3
4. 24√3
1. 16√3
2. 8√3
3. 64√3
4. 24√3
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Correct Answer – Option 1 : 16√3
Given
The altitude of an equilateral triangle = 4√3
Concept
Altitude of an equilateral triangle = (√3/2) × side
Area of an equilateral triangle = (√3/4) × (side)2
Calculation
According to the question
4√3 = (√3/2) × side
⇒ Side = [(4√3) × 2]/√3
⇒ Side = 8 cm
Now,
⇒ Area of an equilateral triangle = (√3/4) × 82
⇒ Area of an equilateral triangle = 16√3 cm2
∴ Area of an equilateral triangle = 16√3 cm2