The area of the shaded region is 25.72 square feet, to the nearest hundredth.
Step 1: Identify the shapes and their dimensions
Rectangle:
Width = 3 feet (from the left edge to the semicircle's diameter)
Height = 2 feet (from the bottom edge to the top of the rectangle)
Semicircle:
Diameter = 3 feet (horizontal line across the shaded area)
Radius = 3 feet / 2 = 1.5 feet (half the diameter)
Step 2: Calculate the area of the rectangle
Area of rectangle = width x height
Area = 3 feet x 2 feet
Area = 6 square feet
Step 3: Calculate the area of the semicircle
Area of semicircle = (π * radius^2) / 2
Area = (π * 1.5 feet^2) / 2
Area ≈ (3.14 * 2.25 feet^2) / 2
Area ≈ 19.72 square feet (rounded to two decimal places)
Step 4: Add the areas of both shapes to find the total area
Total area = area of rectangle + area of semicircle
Total area = 6 square feet + 19.72 square feet
Total area ≈ 25.72 square feet (rounded to two decimal places)
Therefore, you are correct that the area of the shaded region in the image is 25.72 square feet, rounded to the nearest hundredth.