Question Video: Finding the Perimeter of a Composite Shape | Nagwa Question Video: Finding the Perimeter of a Composite Shape | Nagwa

Question Video: Finding the Perimeter of a Composite Shape Mathematics

Determine the perimeter of the shape below.

02:31

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.

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