Question P6 Overlap and cancel
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Mr Kumar stands three identical equilateral triangular wooden blocks, Block A, Block B and Block C, upright in a straight groove on his workbench. Each block rests with its bottom edge lying flat along the groove. Block A is on the left, Block B is in the middle and Block C is on the right. Block B overlaps Block A when seen from the front, and Block B also overlaps Block C, but Block A and Block C do not overlap each other. Measured along the groove:
The shaded parts are the part of Block A that is not hidden by Block B, and the part of Block C that is not hidden by Block B.
Answer
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Two shapes share a region, and the shared part cancels out.
In this one. The blocks are identical, so sliding one onto the next moves its left corner and its right corner by exactly the same distance — right-corner-to-right-corner (52 cm) is also left-corner-to-left-corner, and the whole picture collapses into adding and subtracting along one line.
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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