Question Video: Calculating the Perimeter of a Composite Figure Involving Circles and a Rectangle Mathematics

Determine the perimeter of the figure, using 22/7 to approximate ๐œ‹.

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Video Transcript

Determine the perimeter of the figure, using 22 over seven to approximate ๐œ‹.

The figure weโ€™ve been given is a composite figure. Itโ€™s composed of two semicircles attached to either side of a rectangle. Tracing our finger all the way around the edge of the shape from a given point, we see that the perimeter is composed of a straight edge; a semicircular arc; another straight edge, the same length as the first; and a second semicircular arc, the same length as the previous one.

From the figure, we can see that the length of each straight edge is 42 centimeters. So we can substitute these values directly. But what about the length of these two semicircular arcs? Well, together, these two arcs will form a full circle. And we know the formula for calculating the perimeter or circumference of a circle is ๐œ‹ times its diameter. From the figure, we can see that the diameter of our circle is 49 centimeters. So the circumference of the circle is 49๐œ‹.

Now weโ€™re told in the question that we should use 22 over seven as an approximation for ๐œ‹. This gives 49 multiplied by 22 over seven. And then we can cancel a factor of seven in the denominator with a factor of seven in the numerator, giving seven multiplied by 22. We can work this out using any multiplication method we choose. Here Iโ€™ve shown the column method, and it gives 154. So the perimeter of the figure becomes 42 plus 154 plus 42. Thatโ€™s 238. The units for the perimeter are the same as the units given for the individual lengths in the question. So they are centimeters. Notice that because we used 22 over seven as an approximation for ๐œ‹, we had no need to use a calculator in this question.

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