The height of an equilateral triangle is 7$\sqrt{3}$ cm. What is the area of this equilateral triangle?

49$\sqrt{3}$ cm²

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