Question

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

• A. $5.196{cm}^2$
• B. $0.866{cm}^2$
• C. $3.496{cm}^2$
• D. $1.732{cm}^2$

Answer 1

The correct option is A

$5.196{cm}^2$

An equilateral triangle has all three sides equal to each other. Due to this all the internal angles are of equal degrees, i.e. each of the angles is $60°$

Given

The side of an equilateral triangle $=2\sqrt{3}cm$

We know that

Area of an equilateral triangle $=\frac{\sqrt{3}}{4}\times {\left(side\right)}^2$

$$\begin{gathered} =\frac{\sqrt{3}}{4}\times {\left(2\sqrt{3}\right)}^2 \\ =\frac{\sqrt{3}}{4}\times 12 \\ =3\times \sqrt{3} \\ =3\times 1.732\left(\because \sqrt{3}=1.732\right) \\ =5.196{cm}^2 \end{gathered}$$

Therefore, the area of an equilateral triangle is $5.196{cm}^2$
Hence, option A is correct