Calculate perimeter - Composite figures
Theory
A composite figure is made by joining rectangles, such as an L-shape. Its perimeter is still the distance all the way around, but some sides may not be marked. This Year 5 maths page shows how to find each unmarked side by adding or subtracting the sides that are parallel to it, how to add every side without missing one, and a shortcut for shapes with a corner cut out.
A composite figure is a shape made of two or more simple shapes. The L-shapes and T-shapes here are made of rectangles, and every corner is a right angle.
To find an unmarked horizontal side, compare it with the other horizontal sides: the long bottom side equals the two top pieces added together. Do the same for vertical sides.
Count the sides first. An L-shape has \(6\) sides; a T-shape has \(8\). Your sum must have that many numbers.
Shortcut: when a rectangle has been cut from a corner (or from the corners), pushing the inside edges out rebuilds the full rectangle, so the perimeter equals the perimeter of the surrounding rectangle.
Finding sides and perimeter:
How to find the perimeter of a composite figure
- Find any unmarked sides by adding or subtracting parallel sides.
- Write every side length on the diagram.
- Add all the sides, going around the shape.
- Check with the surrounding rectangle if a corner has been cut out.
| \(13 + 5 + 5 + 6 + 8 + 11\) | \(=\) | \(48\text{ cm}\) |
\(48\) cm.
| \(13 - 8\) | \(=\) | \(5\text{ cm}\) |
| \(11 - 5\) | \(=\) | \(6\text{ cm}\) |
The horizontal step is \(5\) cm and the vertical step is \(6\) cm.
| \(2 \times (13 + 11)\) | \(=\) | \(48\text{ cm}\) |
\(48\) cm, the same as adding all six sides.
| \(15 + 3 + 5 + 7\) | \(=\) | \(30\) |
| \(5 + 7 + 5 + 3\) | \(=\) | \(20\) |
| \(30 + 20\) | \(=\) | \(50\text{ cm}\) |
\(50\) cm. It fits in a \(15\) by \(10\) rectangle, and \(2 \times (15 + 10) = 50\).
(i) Find the two unmarked sides.
(ii) How much fencing goes around it?
| \(40 - 25\) | \(=\) | \(15\text{ m}\) |
| \(35 - 15\) | \(=\) | \(20\text{ m}\) |
| \(40 + 15 + 15\) | \(=\) | \(70\) |
| \(20 + 25 + 35\) | \(=\) | \(80\) |
| \(70 + 80\) | \(=\) | \(150\text{ m}\) |
(i) \(15\) m and \(20\) m
(ii) \(150\) m
| \(37 + 5 + 6\) | \(=\) | \(48\text{ cm}\) |
He left out the two unmarked sides. The perimeter is \(48\) cm.
Common pitfalls
Frequently asked questions
What is a composite figure?
A shape made by joining simpler shapes, such as two rectangles making an L-shape.
How do you find an unmarked side?
Use the parallel sides. If the bottom is \(13\) and the top piece is \(8\), the step is \(13 - 8 = 5\).
How many sides does an L-shape have?
Six. A T-shape has eight.
Is there a quick way for an L-shape?
Yes. Its perimeter equals the perimeter of the rectangle it fits in: \(2 \times (13 + 11) = 48\).
What unit is perimeter measured in?
A unit of length, such as cm or m.