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5.08 Perimeter of composite shapes


Composing a shape

When a shape is made up, or composed, of separate shapes, it's called a composite shape. The lines where they join aren't usually visible, but we can still make out the separate shapes. We can use what we already know, including how to find the perimeter of a polygon, to calculate the perimeter of our composite shape.

When finding the perimeter of composite shapes there are two main approaches.

The first approach is finding the length of all the sides and adding them together like we would for an irregular shape. We can do this by using the lengths we are given to find any missing lengths.

The other approach is less obvious and relies on some visualization. We can see in the image below that the composite shape actually has the same perimeter as a rectangle.

So the perimeter of this composite shape can be calculated as:

Perimeter $=$= $2\times\left(8+13\right)$2×(8+13)
  $=$= $2\times21$2×21
  $=$= $42$42

When using this method it is important to keep track of any sides that do not get moved.

An example of a shape that we need to be careful with is:

Notice that we moved the indented edge to complete the rectangle but we still need to count the two edges that weren't moved.

We can calculate the perimeter of this shape as:

Perimeter $=$= $2\times\left(5+11\right)+2+2$2×(5+11)+2+2
  $=$= $2\times16+4$2×16+4
  $=$= $32+4$32+4
  $=$= $36$36

With our knowledge of the perimeter of simple shapes like rectangles and squares we can often find creative ways to work out the perimeter of more complicated composite shapes.


Practice questions

Question 1

Consider the following figure.

  1. Find the length $x$x.

  2. Find the length $y$y.

  3. Calculate the perimeter of the figure.

Question 2

Find the perimeter of the shape.

Question 3

Find the perimeter of the following figure. Use the $\pi$π button on your calculator, rounding your final answer to one decimal place.



Compare and order real numbers


Solve area and perimeter problems, including practical problems, involving composite plane figures.

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