Question P5–P6 Overlap and cancel
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A rectangular garden PQRS is divided into two rectangular beds by a straight path UV, where U is on PQ and V is on SR (so PUVS and UQRV are the two beds). H is a sprinkler point on PS, D is a sprinkler point on QR, and M is the midpoint of UV. The perimeter of PQRS is 84 m and PS : PQ = 3 : 4. Find (a) PS, and (b) the total area of the shaded triangles HMV and UMD.
Answer
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Two shapes share a region, and the shared part cancels out.
In this one. The two triangles have equal 9 m bases on UV, while their perpendicular heights are PU and UQ, which join to make the full width PQ; therefore the split point U does not affect their total area.
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.
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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