Question

if its perimeter of an equilateral triangle is 180cm find its area

Answer 1

Using the formulas

A=root3 a square /4

P=3a

Solving forA

A=3P2

36=3·1802

36≈1558.84573cm²

Answer 2

Let the side of the given equilateral ∆ be a cm.

Since, perimeter of an equilateral ∆ = 3a

So , according to question we get

3a =180.

→ a = 60.

Now, area of an equilateral ∆ =√3a^2/4 sq.units .

→ area of the given equilateral ∆ = √3×60×60/4 cm^2 = 900√3 cm^2.