Question

The perimeter of an equilateral triangle is 36 cm. The area of the triangle is equal to

• A. $24\sqrt{3}{\text{cm}}^2$
• B. $36{\text{cm}}^2$
• C. $36\sqrt{3}{\text{cm}}^2$
• D. $24\sqrt{2}{\text{cm}}^2$

Answer 1

The correct option is C $36\sqrt{3}{\text{cm}}^2$

Let the side of an equilateral triangle be a.
Given that the perimeter of the equilateral triangle is 36 cm.
$\Rightarrow 3\times Side=36$
$\Rightarrow 3a=36$
$\Rightarrow a=12cm$
$\therefore$ Area of the triangle= $\frac{\sqrt{3}}{4}\times a^2$
$=\frac{\sqrt{3}}{4}\times (12{)}^2$
$=36\sqrt{3}$
Hence, the correct is option (3).