Question

perimeter of an equilateral triangle is 24 cm.Then what is its area​

Answer 1

Answer:

16√3 cm^2

Step-by-step explanation:

Perimeter of equilateral triangle = 24 cm

let the side of equilateral triangle be a cm.

then,

a + a + a = 24 cm

=> 3a = 24 cm

=> a = 8 cm.

Each side of equilateral triangle is 8 cm.

Now you can use pythagoras theorem to find the height of the triangle.

height = √ ( hypotenuse^2 - base^2 )

= √ ( (8 cm)^2 - (4 cm)^2 )

= √ ( 64 cm^2 - 16 cm^2 )

= √ ( 48 cm^2 )

= √48 cm

Area of triangle

= 1/2 × base × height

= 1/2 × 8 cm × √48 cm

= 1/2 × 8 × √(2×2×2×2×3) cm^2

= 1/2 × 8 × 2 × 2 × √3 cm^2

= 16√3 cm^2

If you don't want to do all these stuff then simply put the formula:

Area of equilateral triaangle

= (√3 × a^2) / 4

= (√3 × 64) / 4 cm^2

= √3 × 16 cm^2

= 16√3 cm^2

You will get the same answer.