Question

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

• A. $2\sqrt{3}c{m}^2$
• B. $2\sqrt{2}c{m}^2$
• C. $3\sqrt{3}c{m}^2$
• D. $6\sqrt{2}c{m}^2$

Answer 1

The correct option is A $2\sqrt{3}c{m}^2$

We know altitude of equilateral triangle=$\frac{\sqrt{3}}{2}a$ where a the side of triangle)

$\frac{\sqrt{3}}{2}a=\sqrt{6}\Rightarrow a=\frac{2\sqrt{6}}{\sqrt{2}}\Rightarrow a=2\sqrt{3}$ cm

Then area of equilateral triangle=$\frac{\sqrt{3}}{4}\times (2\sqrt{2}{)}^2=\frac{\sqrt{3}}{4}\times 8=2\sqrt{3}$ sq cm