The height of an equilateral triangle is 7$\sqrt{3}$ cm. What is the area of this equilateral triangle?
Answer & explanation
Correct answer: option 3
We know that,
Area of a equilateral triangle = \(\frac{\sqrt {3}}{4}\) × (side)2
Length of the altitude of an equilateral triangle = \(\frac{\sqrt {3}}{2}\) × (side)
So, according to the question,
Length of the altitude = 7$\sqrt{3}$
\(\frac{\sqrt {3}}{2}\) × (side) = 7$\sqrt{3}$
side = 14
Area of a equilateral triangle = \(\frac{\sqrt {3}}{4}\) × (14)2
= 49$\sqrt{3}$ cm2