How to teach area and perimeter of composite shapes
Year 8 (ages 13 to 14)
A composite shape is made of two or more simple shapes joined or cut from each other. This unit covers finding its area by adding or subtracting the simple parts, and its perimeter by tracing the outer boundary carefully.
How to teach it
- Show how to split an L-shape (or other composite shape) into two rectangles, marking the split clearly on a diagram.
- Practise the 'add the parts' method for shapes made of joined rectangles, and the 'subtract the cut-out' method for a notch removed from a larger shape.
- For perimeter, trace the outer boundary of the composite shape step by step, not just adding the original rectangle's sides.
- Demonstrate why cutting a rectangular notch from a corner leaves the perimeter unchanged, using a labelled example.
- Mix area and perimeter questions on the same composite shapes so students practise choosing the right approach for each.
Worked example
An L-shaped room is a 12 by 15 rectangle with a 5 by 6 rectangle cut from one corner Area = 12 x 15 - 5 x 6 = 180 - 30 = 150 square units
Common mistakes
- Forgetting to subtract the cut-out rectangle's area (or add the joined rectangle's area) rather than treating the shape as one simple rectangle.
- Calculating the perimeter as if it were a simple rectangle's, ignoring the extra step edges of the notch.
- Splitting a composite shape into parts that overlap or leave a gap, so the areas do not add up correctly.
- Mixing up which two dimensions belong to the cut-out piece versus the main rectangle.
Frequently asked questions
How do you find the area of an irregular (composite) shape?
Split the shape into simple rectangles (or other basic shapes), find each part's area separately, then add them together (or subtract, for a notch cut out of a larger shape).
Does cutting a rectangular notch out of a corner change the perimeter?
No. Cutting a rectangular notch from a corner replaces two removed edges with two new step edges of equal total length, so the perimeter of the resulting L-shape equals the original rectangle's perimeter.
How do you find the area of an L-shaped room?
Treat it as a large rectangle with a smaller rectangle cut from one corner: find the big rectangle's area, then subtract the cut-out rectangle's area.
What year is the area and perimeter of composite shapes taught?
In the Australian Curriculum this is a Year 8 skill (AC9M8M01): solving problems about the area and perimeter of irregular and composite shapes.
Practise with free worksheets
Printable worksheets with answer keys that are never wrong.