Question

The area of an equilateral triangle with side ${\displaystyle 2\sqrt{3}}$ cm is ______.

विकल्प

• 5.196 cm² 

• 0.866 cm²

• 3.496 cm²

• 1.732 cm²

Answer 1

The area of an equilateral triangle with side ${\displaystyle 2\sqrt{3}}$ cm is 5.196 cm².

Explanation:

Area of an equilateral triangle of side a is given by ${\displaystyle \frac{\sqrt{3}}{4}{a}^2}$

Given that ${\displaystyle a=2\sqrt{3}}$

Area (Δ) = ${\displaystyle \frac{\sqrt{3}}{4}{a}^2}$

= ${\displaystyle \frac{\sqrt{3}}{4}{\left(2\sqrt{3}\right)}^2}$

= ${\displaystyle \frac{\sqrt{3}}{4}\times 12}$

= ${\displaystyle 3\sqrt{3}}$

= 5.196 cm²