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Triangular blocks — Mr Kumar's workbench
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 distance from the left corner of Block A to the left corner of Block B is 25 cm
- the distance from the left corner of Block C to the right corner of Block B is 5 cm
- the distance from the right corner of Block A to the right corner of Block C is 52 cm
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.
- (a) Find the length of one side of a block.
- (b) Find the total perimeter of the two shaded parts.
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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 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.
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.
Try one like it
Challenging PSLE overlapping shapes 4 identical semicircles overlap in a row. A, B and C are the 3 identical shaded overlaps. The unshaded area is 2125 cm² more than …The 33 problem patterns
All 33 patterns, one to a page — the 19 behind Primary 5 and 6 word problems, and the skills the younger years are built on. The bar model, how to spot it in the question, and the mistake children make. A booklet you can print. Free.
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