Question

if the perimeter of an equilateral triangle is 180 cm . then its area will be​

Answer 1

perimeter of triangle = 3 ( side)

180 =3( side)

side =60

Area of triangle = (side) ³

= 60³

= 216000

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Answer 2

Given :

• Perimeter of Equilateral Triangle is 180 cm.

To Find :

• Area of Equilateral Triangle .

Solution :

Firstly we will find the Side of Equilateral Triangle :

Using Formula :

$\longmapsto\tt\boxed{Perimeter\:of\:Equilateral\:\triangle=3a}$

Putting Values :

$\longmapsto\tt{180=3a}$

$\longmapsto\tt{\cancel\dfrac{180}{3}=a}$

$\longmapsto\tt\bf{a=60\:cm}$

So , The length of the side of Equilateral triangle is 60 cm.

Now ,

$\longmapsto\tt{Side\:(a)=60\:cm}$

Using Formula :

$\longmapsto\tt\boxed{Area\:of\:Equilateral\:\triangle=\dfrac{\sqrt{3}}{4}\times{{a}^{2}}}$

Putting Values :

$\longmapsto\tt{\dfrac{\sqrt{3}}{{\cancel{4}}}\times{{\cancel{60}}}\times{60}}$

$\longmapsto\tt{\sqrt{3}\times{15}\times{60}}$

$\longmapsto\tt\bf{900\sqrt{3}\:{cm}^{2}}$

So , The Area of Equilateral Triangle is 900√3 cm²...