Question

The perimeter of an equilateral triangle is 60cm2
. What is its area

Answer 1

To Find :

The area of an equilateral triangle

Given :

• Perimeter of triangle = 60 cm
• Area = ???

Formula to be applied:

$\tt{ \bull \: area \: of \: equilateral \: \triangle = \frac{ \sqrt{3} }{4} {a}^{2} }$

$\tt{where \: ' a' \: is \: te \: side \: of \: \triangle}$

$\tt{ \bull \: side \: of \: equilateral \triangle = \frac{perimeter}{3} }$

Solution :

Given, Perimeter of triangle = 60 cm

so, side = Perimeter/3

$\implies \tt{side = \frac{60}{3} }$

$\tt{ \implies \: side = 20 \: cm}$

so, side of the triangle = 20 cm

hence, area of the triangle :

$\tt{area = \frac{ \sqrt{3} }{4} \times {a}^{2} }$

$\tt{ \implies \: area = \frac{ \sqrt{3} }{4} \times {20}^{2} }$

$\tt{ \implies \: area = \frac{ \sqrt{3} }{ \cancel{ 4}} \times \cancel{400}}$

$\red { \underline { \boxed{ \tt{area = 100 \sqrt{3} \: c {m}^{2} }}}}$

hence , area of triangle = 100√3 cm²