📐 Perimeter of Compound Shapes

What you’ll learn

1. Shapes Made of RectanglesRecognise a compound (rectilinear) shape as rectangles joined together.Compound shapes like the L and the T are not new mysteries but rectangles pushed together along shared edges. Seeing the rectangles inside makes the whole shape approachable, and the course's question is how far it is around the outside — its perimeter.
2. Perimeter Is a Walk Around the EdgeDefine perimeter as the total distance around a shape and count an L's six sides.Perimeter is the distance an ant walks around the whole outside edge, found by adding every side. An L-shape has six sides, and the twist of compound shapes is that some of those sides are deliberately left unlabelled.
3. The Trap of the Missing SidesUnderstand why adding only the labelled sides gives a wrong perimeter.On compound shapes some sides are blank, and adding only the visible numbers leaves out real parts of the boundary, giving too small an answer. The true task is to work out the missing lengths before adding.
4. The Matching RuleLearn that opposite-direction sides balance, and use it to find missing lengths.Because a shape's outline closes back on itself, all the sides pointing one way total the same as all those pointing the opposite way. A missing side equals the big edge minus the known piece pointing the same direction.
5. Finding a Hidden SideDeduce unlabelled horizontal and vertical sides by subtracting.Using the matching rule, a hidden step is the full bottom minus the flat top, and a hidden drop is the tall edge minus the short edge. Each missing side is found by subtraction, filling in every blank on the shape.
6. Adding Up the Whole BoundaryComplete the two-step method and estimate to check the perimeter.Once the blanks are filled, the perimeter is found by adding every side around the boundary — for the worked L, 28 cm. Estimating the total first gives a safety net that catches large mistakes.
7. A Shape With a NotchSee that cutting a notch adds edges and increases the perimeter.A square notch cut from a rectangle replaces one straight edge with three, so the boundary — and the perimeter — grows rather than shrinks. The two top pieces plus the notch gap still balance the full bottom.
8. The Boundary Always ClosesGeneralise the method and explain why the balancing rule cannot fail.Any rectilinear shape yields to the same routine: trace, find the blanks, fill by matching, then add. The rule holds because a closed boundary must return to its start, forcing widths and heights into balance.

Questions this course answers

Grounded in trusted sources

• Khan Academy — Perimeter of compound shapes (Grade 4–5)
• BBC Bitesize — Perimeter of rectilinear shapes (KS2)
• NRICH (University of Cambridge) — Perimeter reasoning

Every Wunder lesson is built from real, reputable sources — never invented.

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