Answer:
Option 3rd is correct
[tex]4\sqrt{3}[/tex] square feet
Step-by-step explanation:
Perimeter(P) and Area(A) of equilateral triangle is given by:
[tex]P = 3a[/tex]
[tex]A=\frac{\sqrt{3}}{4}a^2[/tex] ....[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:
[tex]P = 3a[/tex]
[tex]12 = 3a[/tex]
Divide both sides by 3 we have;
[tex]4 = a[/tex]
or
a = 4 ft
Substitute in [1] we have;
[tex]A = \frac{\sqrt{3}}{4}(4)^2 =\frac{\sqrt{3}}{4} \cdot 16 =4\sqrt{3} ft^2[/tex]
Therefore, the area of the equilateral triangle is, [tex]4\sqrt{3}[/tex] square feet
