Question

The perimeter of an equilateral triangle is 12 feet. Find the area of the triangle.

8√3 square feet
8 square feet
4√3 square feet

Answer 1

The answer is 4√3 sq. unit

Answer 2

Option 3rd is correct

`4√(3)` square feet

Explanation:

Perimeter(P) and Area(A) of equilateral triangle is given by:

`P = 3a`

`A=(√(3))/(4)a^2` ....[1]

where, a is the side of the equilateral triangle.

As per the statement:

The perimeter of an equilateral triangle is 12 feet

By definition of perimeter:

`P = 3a`

`12 = 3a`

Divide both sides by 3 we have;

`4 = a`

or

a = 4 ft

Substitute in [1] we have;

`A = (√(3))/(4)(4)^2 =(√(3))/(4) \cdot 16 =4√(3) ft^2`

Therefore, the area of the equilateral triangle is,
`4√(3)` square feet