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Library hall — the partition and the shaded triangles
A rectangular library hall JKLM is divided into two reading rooms by a glass partition NO, where N is on JK and O is on ML (so JNOM and NKLO are the two rooms). E is a bookshelf on JM, F is a bookshelf on KL, and W is the midpoint of NO. The perimeter of JKLM is 88 m and JM : JK = 5 : 6. Find (a) JM, and (b) the total area of the shaded triangles EWO and NWF.
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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. The triangles have equal bases on the two halves of NO, while their perpendicular heights add to the full width JK, so the partition's position does not affect their total area.
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.
The 33 problem patterns
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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