Final Answer:
the perimeter and total area of the composite shape is:
B. Perimeter = 46.28 inches, Area = 137.12 square inches**
Step-by-step explanation:
The composite shape consists of a rectangle and a semicircle. To find the perimeter, we add the lengths of all sides. The rectangle has two sides with lengths 10 inches and 6 inches, totaling 22 inches. The semicircle's circumference is calculated as half of the full circle's circumference, given by the formula C = π * d, where d is the diameter.
The diameter is the sum of the rectangle's length and the semicircle's diameter, which is equal to the rectangle's width. So, the semicircle's circumference is π * (10 + 6) = 16π inches. The total perimeter is 22 + 16π inches. Since π is approximately 3.14, the perimeter is approximately 46.28 inches, matching option B.
To find the area, we calculate the sum of the rectangle's area (length * width) and the semicircle's area (π * r^2 / 2). The rectangle's area is 10 * 6 = 60 square inches. The semicircle's radius is half of the rectangle's width, so it's 6 / 2 = 3 inches.
The semicircle's area is π * 3^2 / 2 = 4.5π square inches. Adding the areas of the rectangle and semicircle gives 60 + 4.5π square inches. Substituting π with 3.14, we get approximately 137.12 square inches, matching option B.