The height of an equilateral triangle is $9\sqrt{3} $ cm . What is the area of this equilateral triangle ?
Answer & explanation
Correct answer: option 4
Area of a equilateral triangle = \(\frac{\sqrt {3}}{4}\) × (side)2
The height of the equilateral triangle = \(\frac{\sqrt {3}}{2}\) × (side)
We have,
Height = $9\sqrt{3} $
$9\sqrt{3} $= \(\frac{\sqrt {3}}{2}\) × (side)
side = 18
Area of a equilateral triangle = \(\frac{\sqrt {3}}{4}\) × (18)2
= $ 81 \sqrt{3} cm^2$