Question

If the perimeter of an equilateral triangle is 24 m, then find its area

Answer 1

ANSWER :

Area of the given equilateral triangle is

$16 \sqrt{3} \: \: {m}^{2}$

EXPLANATION :

We know that,

Perimeter of equilateral triangle = 3 ( side )

Also, it is given that the perimeter of equilateral triangle is 24 m.

So,

3 ( side ) = 24

=> side = 24/3

•°• Side = 8 m

Also,

Area of equilateral triangle $\sf = \dfrac{\sqrt{3}}{4} \times (side)^2$

$\sf = \dfrac{\sqrt{3}}{4} \times 8^2$

$\sf = \sqrt{3} \times 16$

$\sf = 16\sqrt{3} \: m^2$

Hence,

Area of the given triangle is $\sf 16\sqrt{3} \:m^2$

$\rule{200}2$

Answer 2

ANSWER:

• Area of Equilateral triangle = 27.71 m²

GIVEN:

• Perimeter of an equilateral triangle is 24 m.

TO FIND:

• Area of equilateral triangle.

SOLUTION:

Equilateral triangle: Triangle whose all sides are equal in length is called equilateral triangle.

Let the side of Equilateral triangle be 'a'.

Perimeter of Equilateral triangle= Sum of the three sides.

=> a+a+a = 24

=> 3a = 24

=> a = 24/3

=> a = 8 m.

Side of Equilateral triangle = 8m. .....(i)

Area of Equilateral triangle is :

$= \dfrac{ \sqrt{3} }{4} \times (side) {}^{2}$

Putting Side = 8 m from ...(i)

$= \dfrac{ \sqrt{3} }{4} \times (8) {}^{2} \\ \\ = \frac{ \sqrt{3} }{4} \times 64 \\ \\ = \sqrt{3} \times 16 \\ = 16 \sqrt{3} \\ = 16 \times 1.732 \\ = 27.712 \\ = 27.71 \: m {}^{2}$

Area of Equilateral triangle = 27.71 m²