Question

find the area of an equilateral triangle whose perimeter is 360 CM​

Answer 1

hey there,

In an equilateral triangle, all the three sides are equal

perimeter =360 cm

therefore, each side will be 360/3=120 cm

Area of an equilateral triangle =√3/4*a^2

a=120 cm

therefore,

= √3/4*120*120

= 3600√3 cm^2

hence, the area of an equilateral triangle is 3600√3 cm^2

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Answer 2

The area of an equilateral triangle = $3600\sqrt{3}$ $cm^{2}$

Step-by-step explanation:

Let 'a' be the side of an equilateral triangle.

Given,

The perimeter of an equilateral triangle = 360 cm

To find, the area of an equilateral triangle = ?

We know that,

The perimeter of an equilateral triangle = 3a

⇒ 3a = 360 cm

⇒ a = $\dfrac{360}{3} cm$

⇒ a = 120 cm

∴ The area of an equilateral triangle = $\dfrac{\sqrt{3}}{4} \times a^2$

= $\dfrac{\sqrt{3}}{4} \times 120\times 120$ $cm^{2}$

= $\sqrt{3} \times 30\times 120$ $cm^{2}$

= $3600\sqrt{3}$ $cm^{2}$

∴ The area of an equilateral triangle = $3600\sqrt{3}$ $cm^{2}$