Question

if its perimeter of an equilateral triangle is 120 cm, what will be its area

Answer 1

this is the answer for your question

Answer 2

QUESTION:

The correct question should be:

If the perimeter of an equilateral triangle is 120 cm, what will be its area?

ANSWER:

The area of the given equilateral triangle will be 692.8 cm².

Given,

The perimeter of an equilateral triangle = 120 cm.

To find,

Area of this triangle.

Solution,

An equilateral triangle is a triangle that has all of its sides equal.

The perimeter of an equilateral triangle can be given as,

$P=3a$     ...(1)

where 'a' is the side of the triangle.

For the given triangle,

P = 120 cm

Substituting in (1) and rearranging, we get,

$3a=120$

⇒ a = 40 cm.

So, each side of the given triangle = 40 cm.

Now, the area of an equilateral triangle is given by,

$A=\frac{\sqrt{3} }{4}( a^{2} )$

Since $a = 40 cm$

$\implies A=\frac{\sqrt{3} }{4}\times (40)^{2}$

$\implies A=\frac{\sqrt{3} }{4}\times (1600)$

$\implies A=\sqrt{3} \times 400$

Taking $\sqrt{3} =1.732$

$A=1.732 \times 400$

⇒ A = 692.8 cm².

Therefore, the area of the given equilateral triangle will be 692.8 cm²