Problem 23 · 2012 Math Kangaroo
Stretch
Geometry & Measurement
area-fractionfoldingsymmetry
A square piece of paper of area 64 cm\(^2\) is folded twice as shown in the picture. What is the area of the two grey sections?
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Answer: D — 16 cm\(^2\)
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Hint 1 of 3
The whole square has area 64 cm\(^2\), so its side is 8 cm; work in those units.
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Hint 2 of 3
Each fold is a line of symmetry, so the two grey pieces are mirror copies that fit into neat triangles.
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Hint 3 of 3
Figure out what fraction of the 8 by 8 square the grey covers, then take that fraction of 64.
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Approach: grey as a fraction of the folded square
- The square has area 64 cm\(^2\), so each side is \(\sqrt{64}=8\) cm.
- Folding twice creases the square into equal symmetric triangular regions, and the two grey sections together cover one quarter of the whole square.
- So the grey area is \(\tfrac{1}{4}\times 64 = \) 16 cm\(^2\) (choice D).
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