Question

What is the area of an equilateral triangle whose side is 8 cm?

• A. $16\sqrt{3}$ $c{m}^2$
• B. $16c{m}^2$
• C. $\sqrt{3}$ $c{m}^2$
• D. $32c{m}^2$

Answer 1

The correct option is A

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

Semi perimeter of a triangle (s) = $\frac{a+b+c}{2}$
$\Rightarrow \frac{8+8+8}{2}=12cm$
Area of a triangle = $\sqrt{s(s-a)(s-b)(s-c)}$
$=\sqrt{12(12-8)(12-8)(12-8)}$
$=\sqrt{12\times 4\times 4\times 4}$
$=\sqrt{3\times 4\times 4\times 4\times 4}$
= $16\sqrt{3}$ $c{m}^2$