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Grid drawing: equal-area triangle without overlap
A trapezium ABCD and a right-angled triangle ABE are drawn on a square grid inside a box. The diagram shows trapezium ABCD and right-angled triangle ABE sharing side AB, with vertices on grid dots. By joining dots on the grid with straight lines, (a) draw another trapezium ABCF such that AF is longer than BC. (b) draw another triangle ABG such that it has the same area as triangle ABE. Triangle ABG must not overlap with trapezium ABCD.
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The pattern behind it: Area and volume foundations
Choose the matching base and perpendicular height, or count equal cube layers before multiplying dimensions.
In this one. Compare grid movements: equal or proportional right-and-up/down movements show parallel lines, which can prove both a trapezium and equal triangle heights.
How to spot it
Look for shapes drawn on a dotted or squared grid, sharing a side or a vertex, with names like ABCD and ABE. Words like "grid", "dots" or "squares" alongside a request to compare areas or heights are the giveaway.
Common mistake
Children measure height by eye along the slanted side of a shape instead of counting the straight up-down grid distance from the base to the opposite vertex, which gives the wrong height whenever a side leans.
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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