Video Transcript
Determine the perimeter of the figure,
using 22 over seven to approximate 𝜋.
The figure we’ve been given is a
composite figure. It’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 𝜋 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
49𝜋.
Now we’re told in the question that we
should use 22 over seven as an approximation for 𝜋. 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 I’ve shown the column method, and it
gives 154. So the perimeter of the figure becomes 42
plus 154 plus 42. That’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 𝜋, we had no need to use a calculator in this question.
