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100 Points! Geometry question. Photo attached. Find the area of the figure. Round to the nearest tenth if necessary. Please show as much work as possible. Thank you!

100 Points! Geometry question. Photo attached. Find the area of the figure. Round-example-1
User ZiglioUK
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1 Answer

5 votes

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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User Samuel Jack
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