Compound Shape Practice Test Worksheets
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.
For children who understand rectangles but panic when the shape is chopped up, joined together, or missing a side.
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What Do Compound Shape Questions Look Like?
Students are given 2D composite shapes such as L, T, U, C, or plus shapes and must calculate their total area or perimeter. Questions test whether students can split shapes into simpler rectangles, subtract cutouts, and account for every outer edge. Here is a worked example.
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.
Step 5: The inner horizontal edge is 6 - 3 = 3 units. For perimeter, trace all six outside edges: 6 + 6 + 3 + 7 + 3 + 13 = 38 units.
Tip: The line used to split the shape is inside it, so do not include that line in the perimeter.
Rules to Help You Solve Compound Shape Questions
As shown in the example above, splitting an irregular outline into standard rectangles keeps calculations manageable. Use these core strategies to handle splits, cutouts, missing side lengths, and complete perimeters across different compound shapes. Diagrams on this page are not to scale; use the labelled lengths rather than measuring the drawings.
▭ Rule 1: Split into rectangles
For L and T shapes, divide the whole shape into non-overlapping rectangles and add their areas.
Example: A 6 × 6 top rectangle plus a 3 × 7 lower rectangle gives area 36 + 21 = 57 square units.
⬚ 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 square units.
↔ Rule 3: Find hidden side lengths
Compare the full width or height with its known parts to find missing lengths. Use symmetry only when it is stated or marked; do not assume lengths are equal just because they look equal.
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.
Two More Worked Examples
Practise finding area by subtracting a cutout rectangle, then watch out for the classic perimeter trap on shapes with inner steps.
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.
Step 5: The upper-right vertical edge is 12 - 5 - 3 = 4 units. The full top edge matches the bottom at 7 units, and both horizontal notch edges are 4 units.
Step 6: Perimeter follows all eight boundary edges: 7 + 4 + 4 + 5 + 4 + 3 + 7 + 12 = 46 units.
Tip: Subtract the notch when finding area, but include its three edges when finding perimeter.
Do Not Miss the Inner Steps
Question: Find the area and perimeter of the plus shape. The shape has both horizontal and vertical lines of symmetry.
Worked Method
Step 1: Split the plus into one vertical bar and two side arms.
Step 2: Symmetry across the horizontal centre line makes the bottom extension 3 units high, matching the top. The vertical bar's height is 3 + 3 + 3 = 9 units, so its area is 3 × 9 = 27.
Step 3: Symmetry across the vertical centre line makes the left arm match the right. Left arm = 2 × 3 = 6, and right arm = 2 × 3 = 6.
Step 4: Total area = 27 + 6 + 6 = 39 units².
Step 5: The perimeter includes all 12 short outside edges: 3 + 3 + 2 + 3 + 2 + 3 + 3 + 3 + 2 + 3 + 2 + 3 = 32 units.
Tip: Trace every inward step around the arms. Counting only the four outermost ends misses part of the perimeter.
