Question

A semi-circle sits on top of a rectangle to form the figure below. Find its area and perimeter. Use 3.14 for .

4 in.
6 in.
O A = 38.13 square inches, P = 32.84 inches
O A = 80.52 square inches, P = 32.84 inches
O A = 38.13 square inches, P = 23.42 inches
O A = 80.52 square inches, P = 23.42 inches

Answer 1

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Answer:

(c) A = 38.13 square inches; P = 23.42 inches

Explanation:

The radius of the circle is half the diameter, so is 3 inches. This means the entire figure will fit in a rectangle 6 inches wide and 4+3 = 7 inches high. The perimeter of such a rectangle is ...

P = 2(L+W) = 2(7+6) = 26 inches

The area of that rectangle is ...

A = LW = (7)(6) = 42 square inches

Then area of the given figure is less than 42 square inches, and the perimeter is less than 26 inches. The only answer choice that matches these bounds is ...

A = 38.13 square inches; P = 23.42 inches