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Three overlapping triangles — the shaded perimeter
Three identical equilateral triangles overlap on a straight line. Given: A to T2's left corner = 18 cm, T3's left corner to T2's right corner = 3 cm, T1's right corner to T3's right corner = 41 cm. Find AB, and the perimeter of the 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. When two identical shapes overlap on a line, the part of one poking out equals the part of the other poking out — they share the same middle. Once you know that, every span on the line is just alone + overlap + alone, and the whole question is addition and subtraction.
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
Standard Area of triangle Two identical right-angled triangles overlap. Their perpendicular sides are 12 cm and 18 cm; the shaded parts total 132 cm². Find …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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