Question Overlap and cancel
A triangular piece of paper XYZ is folded along XP. The visible figure after folding is of triangle XYZ, and the overlap triangle XWP has area 84 cm². Find the area of triangle XYZ.
Answer
224 cm². Check: 5/8 × 224 = 140 cm², and 224 − 84 = 140 cm². Thus the folded visible figure has the stated area, while the overlapped triangle XWP has area 84 cm².
Two shapes share a region, and the shared part cancels out.
In this one. When the flap is folded, its area does not change; the only area no longer counted in the outline is the overlap XWP, so XWP is the missing 1 − 5/8 = 3/8 of the original triangle.
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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