Video Transcript
Determine the perimeter of the shape
below.
We can see that the shape we’ve been
given is a composite figure. It’s made up of these two rectangles
joined together, or perhaps these two rectangles here. We could also think of it as a larger
rectangle, which has had a smaller rectangle cut out of it. In any case, we need to determine its
perimeter.
Now, when calculating the perimeter of a
shape such as this one, it’s a good idea to start in one corner and trace our way all the
way around the edge of the shape to make sure we don’t miss out any of the lengths. Let’s start at point 𝐴. The perimeter will be equal to 𝐴𝐵 plus
𝐵𝐶 plus 𝐶𝐷 plus 𝐷𝐸 plus 𝐸𝐹 plus 𝐹𝐴. And that’s all the lengths we need to
include as we’re now back at our starting point.
We’ve been given on the diagram the first
four of these lengths. They are five, seven, three, and three
centimeters, respectively. But we haven’t been given the lengths
𝐸𝐹 or 𝐹𝐴. We can work them out though. Firstly, 𝐸𝐹 will be the difference
between the two vertical sides of this figure, 𝐴𝐵 minus 𝐶𝐷. That’s five minus three, which is equal
to two centimeters. 𝐹𝐴 will be the difference between the
horizontal sides of the figure. That’s 𝐵𝐶 minus 𝐷𝐸, seven minus
three, which is equal to four centimeters.
So we now have the lengths of all six
edges of our composite figure, and so we can add them together. Five plus seven plus three plus three
plus two plus four is equal to 24. The units for this perimeter, which is a
length, will be the same as the units for the individual lengths. So our answer is 24 centimeters.
Now notice that this perimeter is
actually the same as the perimeter of the full rectangle 𝐴𝐵𝐶𝐺 if we hadn’t removed the
smaller rectangle 𝐹𝐸𝐷𝐺. And the reason for this is that 𝐸𝐷 is
the same as the length we removed, 𝐹𝐺, and 𝐸𝐹 is the same as the length we removed,
𝐷𝐺.
So for this reason, we could actually
have calculated the perimeter of this particular composite figure using the formula twice
the length plus twice the width for the perimeter of the original rectangle 𝐴𝐵𝐶𝐺.
