Answer:
In a 30°-60°-90° right triangle, the length of the shorter leg is 1/2 the length of the hypotenuse, and the length of the longer leg is √3 times the length of the shorter leg. In the equilateral triangle, the perimeter is (2)(4√3)(3) = 24√3, and the apothem is 4.
π(8^2) - (1/2)(24√3)(4)
= 64π - 48√3 square units
= about 117.92 square units