Question

find the area of equilateral triangle whose perimeter is 24.

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Answer 1

Perimeter = 24

For an equilateral tirange, all sides are of equal length. Let the length of each side be 'a'.

a + a + a = 24

a = 8

Area of an equilateral triangle is given by (√3/4)(a^2)

Area = (√3/4)(8^2) = (√3/4)(64) = 16√3

Hence, the area of the given equilateral triangle is 16√3 sq. unit.

Answer 2

Note: An equilateral triangle is a triangle in which all three sides are equal.

Given: Perimeter = 24 cm

Let 'x' be one side of the equilateral triangle

--> x + x + x = 24

--> 3x = 24

--> x = 24/3 = 8

∴ length of each side = 8 cm

Now, we can use Heron's Formula to find the area of an equilateral triangle and that is √3a²/4, where a = length of one side

Area of equilateral triangle = √3a²/4

= (8²)√3/4

= 16√3 cm²

OR

= 27.68 cm² (In decimals)