Question

A rectangular paperboard measuring 27 in long and 17 in wide has a semicircle cut out of it, as shown below. What is the perimeter of the paperboard that

remains after the semicircle is removed? (Use the value 3.14 for pie, and do not round your answer. Be sure to include the correct unit in your answer.)

Answer 1

97.69 in

Explanation:

You want the perimeter of a 17 in by 27 in rectangle that has a semicircular end.

Perimeter

The perimeter of the figure is the sum of the side lengths. The length of the curved side is half the circumference of the circle with the same diameter:

1/2 C = 1/2(πd) = (3.14/2)·(17 in)

The full perimeter is the sum of the lengths of the straight sides and this length of the curved side:

P = 17 + 27 + 17(3.14/2) + 27

P = 2(27) +17(1 +3.14/2) = 97.69 . . . . inches

The perimeter of the figure is 97.69 inches.

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