Question

if perimeter of an equilateral triangle is 180 what will be its area

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Answer 1

Given :-

Perimeter of a equilateral triangle = 180

To Find :-

Area of the triangle.

Analysis :-

At first, we've to find the side of the equilateral triangle.

In order to find that, divide the perimeter by 3. (Since the triangle has 3 sides and the given triangle is equilateral)

Using the formula of area of triangle, substitute the given values and find the area accordingly.

Solution :-

We know that,

• p = Perimeter
• a = Side

Finding the side,

$\underline{\boxed{\sf Side=\dfrac{Perimeter}{3} }}$

Substituting them,

$\sf =\dfrac{180}{3} =60$

Therefore, each side of the equilateral triangle 60.

By the formula,

$\underline{\boxed{\sf Area \ of \ triangle= \dfrac{\sqrt{3} a^{2}}{4} }}$

Substituting their values,

$\sf =\dfrac{\sqrt{3} \times 60 \times 60}{4}$

$\sf =\dfrac{3600\sqrt{3} }{4}$

$\sf =900\sqrt{3}$

Therefore, area of the equilateral triangle is 900√3.