This worksheet applies area and perimeter formulas to irregular and composite shapes, teaching students to break a complex shape into simpler parts to solve it. The worksheet is split into warm-up questions, standard questions and then extension questions to test you.
The concepts it covers:
- A composite shape is made of two or more simple shapes (rectangles, triangles, semicircles) joined together.
- Composite area can be found by adding the areas of the parts, or by finding a larger bounding shape's area and subtracting what's missing.
- Composite perimeter means tracing the shape's outer boundary only — internal edges where two parts join are not part of the perimeter.
- An irregular shape's area can be estimated by overlaying a grid: count whole squares fully inside, and estimate part-squares (e.g. count a half-filled square as 0.5).
- Cutting a notch out of a shape's corner doesn't always change its perimeter — sometimes the removed edge length exactly equals the new edge length added.
What your child will practise:
- Spliting a composite shape into simple shapes (rectangles, triangles, semicircles), find each area, then add them.
- Finding a composite shape's area by subtracting a "missing" piece from a larger bounding shape.
- Tracing a composite shape's outer boundary carefully to find its perimeter, without double-counting internal edges.
- Estimating an irregular shape's area using a grid, counting whole and part squares.
- Applying composite area and perimeter to real contexts, including cost-per-area problems.
Every section opens with a worked example, and the download includes a full answer key with step-by-step solutions and teaching notes on the mistakes students most commonly make.
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