Final answer:
To find the area of the sector, use the formula A = (θ/2) * r², where θ is the angle and r is the radius.
Step-by-step explanation:
To find the area of the sector, we need to find the radius first. Since the diameter is 16 feet, the radius is half of that, which is 8 feet.
Next, we can use the formula for the area of a sector, which is A = (θ/2) * r², where θ is the angle and r is the radius.
Substituting the values, we have A = (5π/6/2) * 8² = (5π/12) * 64 = (40π/12) * 64 = 213.6283 square feet (rounded to four decimal places).