Answer:
105.12 ft²
Explanation:
You want the area of an 8 ft by 10 ft rectangle with a semicircle attached to one of the short sides.
Area
The area of the figure is equal to the sum of the areas of the rectangle and the semicircle.
Rectangle
The rectangle area is ...
A = LW
A = (10 ft)(8 ft) = 80 ft²
Semicircle
The area of the semicircle is ...
A = (1/2)πr²
A = (1/2)(3.14)(4 ft)² = (3.14)(8 ft²) = 25.12 ft²
Total
The total area is the sum of these:
A = 80 ft² +25.12 ft² = 105.12 ft²
The area of the figure is about 105.12 ft².
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Additional comment
A semicircle has the same area as a rectangle with long side equal to the diameter, and short side equal to (π/4) times the radius. This means the figure's area is equivalent to the rectangle formed by adding 4×(π/4) = π to the 10 ft length. This is the calculation shown in the attachment.
A = 1/2πr² = 1/2π(d/2)r = d(r·π/4) . . . . . area of the semicircle
When figures involve rounded or pointed shapes, we often find it convenient to use the appropriate scale factor to convert them to equivalent rectilinear shapes.
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