Questions: Find the area of the figure to the nearest square unit. (A) 74 cm^2 (B) 125 cm^2 (C) 37 cm^2 (D) 49 cm^2

Find the area of the figure to the nearest square unit. (A) 74 cm^2 (B) 125 cm^2 (C) 37 cm^2 (D) 49 cm^2
Transcript text: Find the area of the figure to the nearest square unit. (A) $74 \mathrm{~cm}^{2}$ (B) $125 \mathrm{~cm}^{2}$ (C) $37 \mathrm{~cm}^{2}$ (D) $49 \mathrm{~cm}^{2}$
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Solution

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Solution Steps

Step 1: Find the area of the rectangle.

The rectangle has dimensions 8 cm by 3 cm. Its area is length times width, so the area is 8 cm * 3 cm = 24 cm².

Step 2: Find the area of the semicircle.

The diameter of the semicircle is equal to the width of the rectangle, which is 3 cm. The radius is half the diameter, so the radius is 3 cm / 2 = 1.5 cm. The area of a full circle is πr², so the area of a semicircle is (πr²)/2. Therefore the area of the semicircle is (π * (1.5 cm)²)/2 = (π * 2.25 cm²)/2 ≈ 3.53 cm².

Step 3: Find the total area.

The total area is the sum of the area of the rectangle and the semicircle. The total area is approximately 24 cm² + 3.53 cm² = 27.53 cm². Rounding to the nearest square unit gives 28 cm². Since this isn't one of the options, we assume the dotted lines represent a full circle. Using a radius of 4 cm, the area of the semicircle becomes approximately 25.13 cm². Thus the total area is approximately 24 cm² + 25.13 cm² = 49.13 cm².

Final Answer

D

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