Question

Each side of an equilateral triangle is $8cm$. Its area is

(a) $24c{m}^2$

(b) $24\sqrt{3}c{m}^2$

(c) $16\sqrt{3}c{m}^2$

(d) $8\sqrt{3}c{m}^2$

Answer 1

Area of equilateral triangle $=\frac{\sqrt{3}}{4}{a}^2$ sq. units

Given:

Each side of an equilateral triangle is $\left(a\right)=8cm$

$\Rightarrow$ Area of equilateral triangle $=\frac{\sqrt{3}}{4}(8cm{)}^2$

$=\frac{\sqrt{3}}{4}\times 8cm\times 8cm$

$=\sqrt{3}\times 2cm\times 8cm$

$=16\sqrt{3}c{m}^2$

Hence, Option C is correct.