### Problem DescriptionIn the diagram below of rectangle AFEB and a semicircle with diameter CD, AB = 5 inches, AB = BC = DE = FE, and CD = 6 inches. Find the area of the shaded region, to the nearest hundredth of a square inch.![Diagram](diagram-placeholder)### Analysis and SolutionTo solve for the shaded area within the rectangle AFEB that includes a semicircle, we need to follow these steps:1. **Calculate the area of the rectangle AFEB:** Given the dimensions: - Height of the rectangle (AB): 5 inches - Width of the rectangle (CD = FE): 6 inches Area of the rectangle \(A_{rectangle}\): \[ A_{rectangle} = \text{Height} \times \text{Width} = 5 \times 6 = 30 \, \text{square inches} \]2. **Calculate the area of the semicircle with diameter CD:** To find the area of the semicircle, we first find the area of a full circle with diameter CD: - Diameter (CD): 6 inches - Radius (r): \( \frac{\text{Diameter}}{2} = \frac{6}{2} = 3 \, \text{inches} \) Area of the full circle: \[ A_{circle} = \pi r^2 = \pi (3^2) = 9\pi \, \text{square inches} \] Area of the semicircle \(A_{semicircle}\): \[ A_{semicircle} = \frac{A_{circle}}{2} = \frac{9\pi}{2} \approx \frac{28.27}{2} = 14.14 \, \text{square inches} \]3. **Calculate the area of the shaded region (rectangle minus semicircle):** \[ A_{shaded} = A_{rectangle} - A_{semicircle} = 30 - 14.14 = 15.86 \, \text{square inches} \]### Answer:The area of the shaded region is approximately **15.86 square inches**.

Name: ### Problem DescriptionIn the diagram below of rectangle AFEB and a s
Uploaded: 2024-03-20T06:47:08.000Z
Channel: Bartleby
Description: ### Problem DescriptionIn the diagram below of rectangle AFEB and a semicircle with diameter CD, AB = 5 inches, AB = BC = DE = FE, and CD = 6 inches. Find the area of the shaded region, to the nearest hundredth of a square inch.![Diagram](diagram-pl