Calculate perimeter - Composite figures
Theory
To find the perimeter of a composite figure, walk right around the outline and add every side. Find any unmarked side first — it equals the long base minus the other runs.
A composite figure, such as an L-shape, is made of rectangles and has more than four sides.
Every side must be counted once, so follow the outline right around and return to the start.
A missing side is found by subtraction: the shorter runs together equal the longer one opposite them.
An unmarked side is found from the sides opposite it.
| Known | Unmarked side |
|---|---|
| base \(12\), top run \(5\) | \(12-5=7\) |
| base \(16\), top run \(7\) | \(16-7=9\) |
How to find a composite perimeter
- Find any unmarked side by subtracting the shorter runs from the longer one.
- Add every side, going right around the outline.
- Check against the bounding rectangle if the shape is an L.
| \(P\) | \(=\) | \(8+2+5+4+3+6=28\) |
The perimeter is \(28\) cm.
| \(\text{side}\) | \(=\) | \(12-5=7\) |
The unmarked side is \(7\) cm.
| \(P\) | \(=\) | \(2\times(15+9)=48\) |
The perimeter is \(48\) cm.
| \(\text{side}=16-7=9\) | \(\rightarrow\) | \(P=16+4+9+6+7+10=52\) |
The perimeter is \(52\) cm.
Common pitfalls
Frequently asked questions
How do you find the perimeter of an L-shape?
Add every side going right around the outline. An L-shape has six sides, so all six must be included.
How do you find a missing side?
The shorter runs on one side together equal the longer side opposite them, so subtract. If the base is \(12\) and the top run is \(5\), the missing run is \(12-5=7\).
Why does an L-shape match a rectangle?
Every horizontal side lies along the top or bottom of the surrounding rectangle, and the same is true of the vertical sides, so the perimeters are equal.
How many sides does a composite figure have?
More than four. A simple L-shape has six, and each one must be counted once when adding up the perimeter.