Question

One side of an equilateral triangle is 6 cm. Its area by using Heron's formula is

• A. $9$ ${cm}^2$
• B. $3$ ${cm}^2$
• C. $9\sqrt{3}$ ${cm}^2$
• D. $3\sqrt{8}$ ${cm}^2$

Answer 1

The correct option is C $9\sqrt{3}$ ${cm}^2$

$a=6cm$, $b=6cm$, $c=6cm$
$\therefore s=\frac{a+b+c}{2}=\frac{6+6+6}{2}=9cm$
$\therefore$ Area of the equilateral triangle
$=\sqrt{s(s-a)(s-b)(s-c)}$
$=\sqrt{9(9-6)(9-6)(9-6)}$
$=\sqrt{9\left(3\right)\left(3\right)\left(3\right)}$
$=9\sqrt{3}{cm}^2$