Since this is a equilateral triangle,
each angular side = 60°
60° ÷ 2 = 30°
By Toa Cah Soh method,
using Cah,
cos30° = A / 4
A = 4cos30
A = √12 ft.
By Pythagoreans' Theorem,
4² - √12² = h²
h² = 4
h = 2 ft.
Total area
= ½ × √12 × 2 × 6
= 6√ 12
6√12 = 12√3
Answer is B.