Answered

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

Verified Answer :

khankareem

The answer is 4√3 sq. unit

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

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