Question

The perimeter of equilateral triangle is 180 cm , find its area? ​

Answer 1

Answer:

The area of the triangle is 900√3 cm²

Answer 2

Given:-

→Perimeter of an equilateral triangle=180cm

To find:-

→Area of the triangle

Solution:-

We know that in an equilateral triangle,

all sides are equal.

Let the sides of the equilateral triangle be

'a' cm each.

Sum of 3 angles of a triangle=180°

→Perimeter of a triangle=Sum of 3 sides

=>a+a+a=180

=>3a=180

=>a=180/3

=>a=60cm

Hence,three sides of the equilateral triangle are

60cm each.

Now,we know that area of an equilateral triangle with side 'a' is given by:-

=>∆ = √3a²/4 sq.units

=>√3×60×60/4

=>√3×60×15

=>900√3 cm²

Thus,area of the equilateral triangle is

900√3 cm².

Some Extra Information:-

•Height of an equilateral triangle with side

'a' is given by:-

=>√3a/2 units

Proof:-

Area of an equilateral triangle with side a:-

=>∆=√3a²/4

=>(√3/4×a²)

=>(1/2×a×√3a/2)

Area of a triangle:-

=>(1/2×base×height)

=>height=√3a/2 units.