Question P5–P6 Overlap and cancel
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The perimeter of one trapezium is 96 cm. Three identical trapeziums are joined edge to edge to form a figure whose perimeter is 204 cm. Find the length of PQ, the edge along which they are joined.
Answer
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Two shapes share a region, and the shared part cancels out.
In this one. Joining never destroys edge — it only moves edge from the outside to the inside, so the drop in perimeter (288 - 204 = 84) is exactly the edge that went inside: 2 joins x 2 edges = 4 copies of PQ.
Shapes are joined, stacked, or have a piece cut off, and the question compares a perimeter or length before and after, rather than asking for an area from scratch.
Children assume perimeter changes the same way area does. Joining shapes or cutting off a corner can leave the perimeter unchanged, or change it by a different amount from the area.
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