Final answer:
The area of the shaded region is 87.48 sq ft. The process of determining the area of the shaded region involves calculating the area of the larger shape and subtracting the area of the smaller shape. The option b is correct as it is near to calculated value.
Step-by-step explanation:
The process of determining the area of the shaded region involves calculating the area of the larger shape and subtracting the area of the smaller shape.
The larger shape, a square with a side length of 12 ft, has an area of 12 ft * 12 ft, yielding 144 sq ft.
The smaller shape, a semicircle with a radius of 6 ft, has an area calculated as 0.5 * (3.14 * 6 ft)^2, resulting in 0.5 * 113.04 sq ft, equivalent to 56.52 sq ft.
Consequently, the area of the shaded region is derived by subtracting the smaller shape's area from the larger shape's area: 144 sq ft - 56.52 sq ft, culminating in a shaded area of 87.48 sq ft.
This method provides a systematic approach to computing the area of the designated region within the composite shape.
Therefore, the option b is correct as it is near to calculated value.