34.5k views
4 votes
Find the perimeter and total area of the composite shape shown below. All measurements are given in inches. Use a = 3.14 in any formulas used. A.Perimeter = 52.56 inches, Area = 137.12 square inches B.Perimeter = 46.28 inches, Area = 137.12 square inches C.Perimeter = 52.56 inches, Area = 162.24 square inches D.Perimeter = 65.12 inches, Area = 162.24 square inches

User Vik
by
8.3k points

1 Answer

1 vote

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.

User Ashouri
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.