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P4–P5 Overlap and cancel

Overlapping squares

Two different squares overlap in an unshaded square. Their full width is 10 cm, and shaded area A is 24 cm² greater than shaded area B. Find the unshaded 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. The overlap sits inside both squares, so taking it off both cancels it — the difference of the shaded parts is just the difference of the whole squares.

Counted twiceA + Bgroup Athe two in bothgroup Bthe same two againCounted oncetake the shared part offin all5 + 4 − 2 = 7

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.

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