Rectangle ACEG — the shaded triangles
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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The pattern behind it: Overlap and cancel
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.
How to spot it
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.
Common mistake
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.
Try one like it
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All 33 patterns, one to a page — the 19 behind Primary 5 and 6 word problems, and the skills the younger years are built on. The bar model, how to spot it in the question, and the mistake children make. A booklet you can print. Free.
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