Question

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

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

Answer 1

Answer: (A)

5.196cm25.196 cm^2

We know that, Area of equilateral triangle is $\frac{\sqrt{3}}{4}$ $(side{)}^2$

Here, sides of the given equilateral triangle $=2\sqrt{3}cm$

So, area of the triangle $=$ $\frac{\sqrt{3}}{4}$ $(2\sqrt{3}cm{)}^2$

$=$ $\frac{\sqrt{3}}{4}$ $\times$ $2^2(\sqrt{3}{)}^{2}c{m}^2$

$=$ $\frac{\sqrt{3}}{4}$ $\times$ $4\left(3\right)c{m}^2$

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

$=$ $3\times 1.732c{m}^2$ [$\because \sqrt{3}=1.732$ ]

$=5.196c{m}^2$ (approximately)

Therefore, the area of the required equilateral triangle is $5.196c{m}^2$

Hence, Option $B$ is correct.