Question

If its perimeter of an equilateral triangle is 180cm, what will be its area?

Answer 1

As we know that the perimeter of equilateral triangle = 3*side

180 = 3*side

180/3 = side

60 = side

Now,

Area of equilateral triangle = [tex]side^{2} \frac{\sqrt{3}}{4} [/tex]

Now,

Area  of equilateral triangle = $60^{2} \frac{ \sqrt 3}{4}$

Then,

Area of equilateral triangle = $3600 \frac{\sqrt{3}}{4}$

 Area of equilateral triangle = $900 \sqrt{3}$ $cm^{2}$



i hope this will help you

-by ABHAY

Answer 2

Hey friend, Harish here.

Here is your answer:

Given that,

Perimeter = 180 cm. 

To find, 

The area of the Equilateral triangle.

Solution,

We know that, Perimeter of equilateral triangle = 3 × (side)

⇒ $3\times (side)= 180$

⇒ $(side) = \frac{180}{3} = 60.$

Now, We know that,

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

Here , a = side of triangle = 60cm.

Then,

⇒ $Area = \frac{ \sqrt{3}\times 60^{2} }{4} = \frac{3600 \sqrt{3} }{4} = 900 \sqrt{3}\ cm^{2}$

Therefore area of the triangle  is 900√3 cm².
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Hope my answer is helpful to you.