Question

If the altitude of an equilateral triangle is $\sqrt{6}$, then the area is:

• A. $2\sqrt{2}$
• B. $2\sqrt{3}$
• C. $3\sqrt{3}$
• D. $6\sqrt{2}$
• E. 12

Answer 1

Answer: (B)

$2\sqrt{3}$

Let 'a' be the side of equilateral triangle.

Altitude of an equilateral triangle = $\sqrt{6}$

$\frac{\sqrt{3}}{2}a=\sqrt{6}⟹a=2\sqrt{2}$

Arc $=\frac{\sqrt{3}}{4}{a}^2=\frac{\sqrt{3}}{4}\times 8=2\sqrt{3}$