Problem 25 · 2012 Math Kangaroo
Stretch
Spatial & Visual Reasoning
foldingareasymmetry
A rectangle ABCD with dimensions 16 cm by 4 cm was folded along the line MN so that corner C meets corner A. What is the area of the Pentagon ABNMD'?
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Answer: D — 47 cm²
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Hint 1 of 2
The crease MN is the perpendicular bisector of AC, since C folds onto A.
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Hint 2 of 2
Find where the crease meets the top and bottom, then total the pentagon's area.
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Approach: locate the crease, then add up the pentagon with the shoelace formula
- Set B = (0,0), A = (0,4), D = (16,4), C = (16,0); folding C onto A means MN is the perpendicular bisector of AC.
- That line meets the bottom at N = (7.5, 0) and the top at M = (8.5, 4); reflecting D over it gives the new corner D'.
- The pentagon A–B–N–M–D' then has area, by the shoelace formula, equal to 47 cm² (D).
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