Find the area of an equilateral triangle (regular 3-gon) with the given measurement. 6-inch apothem A sq. in.?

To find the area of an equilateral triangle using the apothem, the formula is ( \text{Area} = \frac{1}{2} \times \text{Perimeter} \times \text{Apothem} ). For an equilateral triangle with side length ( s ), the perimeter is ( 3s ). The apothem ( a ) can be related to the side length by ( a = \frac{s \sqrt{3}}{6} ). Given an apothem of 6 inches, the side length can be calculated as ( s = \frac{6 \times 6}{\sqrt{3}} = 12\sqrt{3} ). Thus, the area is ( \frac{1}{2} \times 3(12\sqrt{3}) \times 6 = 108\sqrt{3} ) square inches.