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Tarpaulins — P, Q and R overlap on the floor
Three tarpaulins P, Q and R are spread out on a warehouse floor and overlap one another. The combined area of Q and R is of the area of P. Where P overlaps Q, the overlapping part is of Q's area. Where P overlaps R, the overlapping part is of R's area. Altogether, the shaded (overlapping) part of P makes up of P's area. Find P : Q : R.
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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. Compare the actual overlap with half of all of Q + R: the shortfall is exactly one quarter of Q.
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
Challenging PSLE overlapping shapes 4 identical semicircles overlap in a row. A, B and C are the 3 identical shaded overlaps. The unshaded area is 2125 cm² more than …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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