Question

find the area of an equilateral triangle whose side is 4 cm

Answer 1

The area of an equilateral triangle is $\mathbf{4\sqrt{3} \ cm^{2}}$

Step-by-step explanation:

• Given data

        Side of equilateral triangle (a) = 4 cm

• We know formula of equilateral triangle is given below

        $\mathbf{\textrm{Area of equilateral triangle }=\frac{\sqrt{3}}{4}\times Side^{2}}$

• $\mathbf{\textrm{Area of equilateral triangle }=\frac{\sqrt{3}}{4}\times a^{2}}$

• $\mathbf{\textrm{Area of equilateral triangle }=\frac{\sqrt{3}}{4}\times 4^{2}}$

        On cancel out 4 in numerator and denominator, we get

• $\mathbf{\textrm{Area of equilateral triangle }=4\sqrt{3} \ cm^{2}}$ This is the area of equilateral triangle.

Answer 2

$\huge{\underline{\underline{\bf{Solution}}}}$

$\rule{200}{2}$

$\tt Given\begin{cases} \sf{Side \: of \: equilateral \: triangle = 4 \: cm} \end{cases}$

$\rule{200}{2}$

$\Large{\underline{\underline{\bf{To \: Find :}}}}$

We have to find the area of the equilateral triangle.

$\rule{200}{2}$

$\Large{\underline{\underline{\bf{Explanation :}}}}$

We know the formula to find the area of the equilateral triangle when side is given

$\Large{\star{\boxed{\sf{Area = \frac{\sqrt{3}}{4} \times a^2}}}}$

_______________[Put Values]

$\sf{→Area = \frac{\sqrt{3}}{4} \times (4)^2} \\ \\ \sf{→Area = \frac{\sqrt{3}}{\cancel{4}} \times \cancel{16}} \\ \\ \sf{→Area = \sqrt{3} \times 4} \\ \\ \sf{→ Area = 4\sqrt{3} \: cm^2}$

$\Large{\star{\boxed{\sf{Area = 4\sqrt{3} \: cm^2}}}}$