Question Video: Finding the Perimeter of a Semicircle | Nagwa Question Video: Finding the Perimeter of a Semicircle | Nagwa

Question Video: Finding the Perimeter of a Semicircle Mathematics • Second Year of Preparatory School

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Work out the perimeter of the semicircle, giving your answer accurate to two decimal places.

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Video Transcript

Work out the perimeter of the semicircle, giving your answer accurate to two decimal places.

We’re asked to calculate the perimeter of this semicircle, which is the distance all the way around its edge.

The perimeter of a semicircle consists of two parts: the length of its straight edge and the length of its curved arc. We’re given that the length of the straight edge, which is the diameter of the semicircle, is nine units. We then recall that as the circumference of a circle is equal to 𝜋 times its diameter, the length of the arc of a semicircle is half this value. So it’s equal to 𝜋𝑑 over two.

Substituting nine for the diameter of the semicircle and the length of the straight edge gives that the perimeter of the semicircle is equal to nine plus nine 𝜋 over two. Evaluating this on a calculator gives nine plus 14.137 continuing, which is 23.137 continuing. We’re asked to give the answer to two decimal places, so we need to round up. We’ve found that the perimeter of the semicircle, to two decimal places, is 23.14 length units.

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