Answer:
25.7 square units
Explanation:
You want the area of a composite figure consisting of a 4×8 rectangle with a semicircle of diameter 4 removed.
Semicircle
The area of a semicircle with diameter 4 units is ...
A = 1/2πr² = 1/2π(d/2)²
The area of the semicircle in the figure is ...
A = 1/2π(2²) = 2π ≈ 6.3 . . . . square units
Rectangle
The area of the full rectangle without the semicircle removed is the product of its length and width:
A = LW
A = 8×4 = 32 . . . . square units
Figure
The given figure is a rectangle with a semicircle removed, so its area is the difference between the rectangle area and the semicircle area:
A = rectangle - semicircle
A = 32 -6.3 = 25.7 . . . . square units
The area of the figure is about 25.7 square units.