Question P6 Overlap and cancel
Rectangle ACEG is split by BF into rectangles ABFG and BCEF. H is on AG, D is on CE, X is the midpoint of BF. Perimeter of ACEG = 90 cm and AG : AC = 4 : 5. Find (a) AG, and (b) the area shaded — triangles HXF and BXD.
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Two shapes share a region, and the shared part cancels out.
In this one. Both shaded triangles have their base on the same line BF and X is its midpoint, so the two bases are equal (10 cm each) and the two heights are AB and BC — which add to the whole side AC. Where B sits on AC never matters.
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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