Question

The perimeter of an equilateral triangle is 24 cm. Find its area

Answer 1

Required Answer :

The area of equilateral triangle = 16√3 cm²

Given :

• Perimeter of an equilateral triangle = 24 cm

To find :

• Area of the equilateral triangle

Solution :

Here, in the question we are provided with the perimeter of the equilateral triangle and we need to calculate the area. As we know that equilateral triangle has all its side equal to each other. So, firstly we will calculate the value of the side of the triangle and then by using the formula of area of equilateral triangle we will calculate the required answer.

Formula of perimeter of equilateral triangle :-

• Perimeter = 3 × a

where,

• a denotes the side of the triangle

Substituting the given values :

→ 24 = 3 × a

→ 24/3 = a

→ 8 = a

The side of the equilateral triangle = 8 cm

Now, calculating the area of the equilateral triangle :

Using formula,

• Area of equilateral triangle = √3/4 a²

Substituting the given values :

→ Area of triangle = √3/4 × (8)²

→ Area of triangle = √3/4 × 8 × 8

→ Area of triangle = √3 × 2 × 8

→ Area of triangle = 16√3

Therefore, the area of equilateral triangle = 16√3 cm²

Answer 2

Answer:

27.712 cm²

Step-by-step explanation:

Perimeter of equilateral triangle = 24 cm

Side(a)=Perimeter/3=24cm/3= 8cm

Area = √3/4 a²= √3/4×(8)² cm ³

= √3×16 = 16 (1.732) cm³

= 27.712 cm²