Compound Shape Practice
Compound shape questions ask you to find area and perimeter when a shape has been built from rectangles. The key is to split the shape into clear rectangles, or subtract a missing cutout from a larger rectangle.
The Rules Every Compound Shape Question Uses
The practice papers use L, T, U, C, and plus shapes. The same core moves appear again and again: split, subtract, infer missing sides, and trace the full outside edge.
▭ Rule 1: Split into rectangles
For L and T shapes, divide the shape into rectangles and add their areas.
Example: A 6 × 6 top rectangle plus a 3 × 7 lower rectangle gives area 36 + 21 = 57.
⬚ Rule 2: Subtract cutouts
For C and U shapes, start with the outside rectangle, then subtract the missing rectangle.
Example: 7 × 12 outside minus a 4 × 5 cutout gives 84 - 20 = 64.
↔ Rule 3: Find hidden side lengths
Opposite matching lengths often reveal hidden edges before you calculate the perimeter.
Example: In a U-shape with bottom 13 and inner gap 7, the two top side widths total 6.
🔁 Rule 4: Trace every outside edge
Perimeter means the full outside path, including inward steps around notches and arms.
Example: A C-shape perimeter can include eight sides, not just the four sides of its bounding box.
How to Solve Compound Shape Questions
Three useful moves: split into rectangles, subtract a cutout, and be careful not to miss the inner perimeter edges.
1. Split an L-Shape into Two Rectangles
Question: Find the area and perimeter of the compound shape.
Worked Method
Step 1: Split the shape into a top rectangle and a bottom-left rectangle.
Step 2: Top rectangle = 6 × 6 = 36.
Step 3: Bottom-left rectangle height = 13 - 6 = 7, so its area is 3 × 7 = 21.
Step 4: Total area = 36 + 21 = 57 units².
Tip: For perimeter, trace all six outside edges: 6 + 6 + 3 + 7 + 3 + 13 = 38 units.
2. Subtract the Missing Rectangle
Question: Find the area and perimeter of the C-shape.
Worked Method
Step 1: Treat the shape as a 7 × 12 rectangle with a 4 × 5 notch removed.
Step 2: Bounding rectangle = 7 × 12 = 84.
Step 3: Notch cutout = 4 × 5 = 20.
Step 4: Total area = 84 - 20 = 64 units².
Tip: Perimeter still follows the notch: 7 + 4 + 4 + 5 + 4 + 3 + 7 + 12 = 46 units.
3. Do Not Miss the Inner Steps
Question: Find the area and perimeter of the plus shape.
Worked Method
Step 1: Split the plus into one vertical bar and two side arms.
Step 2: Vertical bar = 3 × 9 = 27.
Step 3: Left arm = 2 × 3 = 6, and right arm = 2 × 3 = 6.
Step 4: Total area = 27 + 6 + 6 = 39 units².
Tip: The perimeter includes all 12 short outside edges: 3 + 3 + 2 + 3 + 2 + 3 + 3 + 3 + 2 + 3 + 2 + 3 = 32 units.
Before You Buy
Want to check the level and layout first? Download the free 3-question sample. It uses the same question style, printable format, and answer-key approach as the full pack.
Download Free Sample PDFGet the Full Practice Pack
The full Deconstructing Shapes pack contains 90 questions across 3 printable test sets. Students practise finding area and perimeter for L, T, U, C, and plus-shaped compound shapes.
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