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Area of a rectangle after two semicircles are cut out

Two equal half-circles make one full circle

When two semicircles of the same radius are removed from a rectangle without overlapping, add their areas as one whole circle. If their common diameter is $d$ , subtract $π (d /2)^{2}$ from the rectangle area.

Problem

A rectangle is $31$ cm long and $16$ cm wide. Two semicircles are cut from its left and right sides; each has diameter $16$ cm. Find the remaining area using $π = 3.14$ .

Answer

295.04 cm^{2}

The two cutouts together have the area of a radius-8 cm circle.

Step-by-step solution

1. Find the rectangle area

A_{rect} = 31 \cdot 16 = 496 cm^{2} .

2. Combine the cutouts

Each semicircle has radius $16/2 = 8$ cm. Together they form one full circle in area:

A_{cut} = 3.14 \cdot 8^{2} = 200.96 cm^{2} .

3. Subtract

A_{remaining} = 496 - 200.96 = 295.04 cm^{2} .

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