Question P6 Overlap and cancel
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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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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.
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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