Problem 6 · 2014 Math Kangaroo
Medium
Spatial & Visual Reasoning
paper-cuttingarea-decomposition
Wanda has lots of pages of square paper, each with an area of 4. She cuts each page into right-angled triangles and squares (see the left-hand diagram). She takes a few of these pieces and forms the shape in the right-hand diagram. What is the area of this shape?
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Answer: E — 6
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Hint 1 of 2
Each whole page has area 4, so work out the area of each small piece she cuts.
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Hint 2 of 2
Add up the areas of the pieces that make the right-hand shape, regardless of how they are turned.
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Approach: count the area contributed by each cut piece
- Each page is a square of area 4, i.e. side 2; the cuts make a big right triangle of area 2, a unit square of area 1, and a small right triangle of area 1.
- The dog shape is built from these pieces, so just add the areas of the pieces used: it is made up of unit squares and triangles of area 1 plus a couple of the area-2 triangles.
- Adding the areas of all the assembled pieces totals an area of 6.
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