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

Answer: (A)

$2\sqrt{3}c{m}^2$

In an equilateral triangle height$=\frac{\sqrt{3}a}{2}$

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

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

Area of the triangle $=\frac{1}{2}\times Base\times Height$

$\Rightarrow \frac{1}{2}\times \frac{2\times \sqrt{6}}{\sqrt{3}}\times \sqrt{6}=\frac{6}{\sqrt{3}}=\frac{2\times \sqrt{3}\times \sqrt{3}}{\sqrt{3}}=2\sqrt{3}c{m}^2$