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 shaded area. Take π = 3.14. Find (a) the perimeter of the unshaded part, (b) the total shaded area.
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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. An overlap belongs to two shapes at once — so adding all four semicircles counts each shaded part twice, and cutting the shaded parts out turns every arc into an edge.
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 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 = …The 33 problem patterns
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