Problem 17 · 2015 Math Kangaroo
Stretch
Geometry & Measurement
area-decompositiongrid-counting
Luca wants to cut the shape in figure 1 into equally sized small triangles (like those in figure 2). One of these triangles is already drawn on figure 1. How many of these triangles will he get?
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Answer: D — 15
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Hint 1 of 2
Notice that one little triangle is exactly half of a small grid square.
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Hint 2 of 2
If you know how much room the big shape covers in grid squares, two triangles fit in each square.
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Approach: fit the half-square triangles into the shape
- Each little triangle is half of a small grid square, so two of them fill one square.
- The big shape covers seven-and-a-half squares of room, and two triangles fit in every square.
- Doubling seven-and-a-half gives 15 little triangles.
- Luca gets 15 triangles.
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