Question

A semi-circle sits on top of a rectangle to form the figure below. Find its area and perimeter. Use 3.14 for π. Dimensions: Rectangle: 2 inches by 4 inches Semi-circle on top Options: A) Area = 20.33 square inches, Perimeter = 14.28 inches B) Area = 14.28 square inches, Perimeter = 20.56 inches C) Area = 14.28 square inches, Perimeter = 14.28 inches D) Area = 33.12 square inches, Perimeter = 20.56 inches

Answer 1

The total area of the figure is 9.57 square inches and the total perimeter is 11.14 inches. None of the provided options exactly match the correct answer.

Step-by-step explanation:

To solve for the area and perimeter of this composite figure, you need to calculate for both the rectangle and the semi-circle then sum them up. The area of the rectangle is length * width = 2 inches * 4 inches = 8 square inches. The area of the semi-circle is (1/2) * π * r^2. Given that the rectangle's width is also the diameter of the semi-circle, the radius of the semi-circle is 2 inches / 2 = 1 inch. Therefore, the area of the semi-circle is (1/2) * 3.14 * (1 inch)^2 = 1.57 square inches.

So, the total area of the figure equals the sum of the rectangle's and semi-circle's areas = 8 square inches + 1.57 square inches = 9.57 square inches.

The perimeter of this composite figure is the sum of the rectangle's two lengths and the semi-circle's circumference (because the rectangle's widths are the same as the diameters of the semi-circle). So the perimeter = 2 * (length of rectangle) + π * radius = 2 * 4 inches + 3.14 * 1 inch = 8 inches + 3.14 inches = 11.14 inches.

Therefore, none of the given options exactly match the correct answer. The closest one could be option C but it is not exactly correct.

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