Answer:
38.9 in²
Explanation:
You want the area of the composite figure that is an 8-inch square with a semicircle removed.
Semicircle area
The missing semicircle has a diameter of 8 in, so a radius of 4 in. The area of that half-circle is ...
A = 1/2πr² = (π/2)(4 in)² = 8π in² ≈ 25.1 in²
Square area
The area of the square without the semicircle removed is ...
A = s² = (8 in)² = 64 in²
Composite area
After removing the semicircle from the square, the remaining area is ...
A = square area - semicircle area
A = 64 in² -25.1 in² = 38.9 in²
The area of the figure is about 38.9 square inches.
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