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.
