Question

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

Answer 1

The answer is 4√3 sq. unit

Answer 2

Answer:

Option 3rd is correct

$4\sqrt{3}$ square feet

Step-by-step explanation:

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

$P = 3a$

$A=\frac{\sqrt{3}}{4}a^2$             ....[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;

$A = \frac{\sqrt{3}}{4}(4)^2 =\frac{\sqrt{3}}{4} \cdot 16 =4\sqrt{3} ft^2$

Therefore, the area of the equilateral triangle is,  $4\sqrt{3}$ square feet