Question

If the perimeter of an equilateral triangle is 60cm, then find its area

Answer 1

HEY MATE HERE IS YOUR ANSWER

Given :

Perimeter of equilateral triangle = 60cm

To find :

Area of equilateral triangle

Formula To use in This question

Perimeter of equilateral triangle = p= 3 a

Here "a" is side

Area of equilateral triangle =
$\frac{ \sqrt{4} }{3} {a}^{2}$
Solution :

$a = \sqrt{3} \times \frac{ {p}^{2} }{36} = \sqrt{3} \times \frac{ {60}^{2} }{36}$
= 173.20508 cm^2

Therefore area of equilateral triangle is 173.20508cm^2


HOPE IT WILL HELP YOU

Answer 2

Heya !!

$\text{Let the side of the triangle be \alpha } \\\\ \\\\\text{And, Perimeter of triangle is 60 cm.} \\\\\\\\According \: \: to \: \: the \: \: question, \\\\ \\\\\alpha + \alpha + \alpha = 60 \\\\ \\\\\implies 3 \alpha = 60 \\\\\implies \alpha = \dfrac{60}{3} \\\\\implies \aplha = 20 \: \:cm$

$\text{Now, area of equilateral \Delta = \dfrac{\sqrt{3}}{4} \times {\alpha}^{2} }\\\\= \dfrac{\sqrt{3}}{4} \times {20}^{2}\\\\= \dfrac{\sqrt{3}}{4} \times {400}\\\\= \sqrt{3} \times 100 \\\\= 100 \times 1.732 \\\\= \boxed{173.2 \: \: cm^2}$

Hope it helps !!