Problem 4 · 2020 Math Kangaroo
Easy
Geometry & Measurement
area-fractionarea-decomposition
One square was divided into four equal squares, containing equal colored squares and equal colored triangles, as shown in the picture. What fraction of the original square does the colored part represent?
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Answer: B — 12
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Hint 1 of 2
The big square is four equal small squares; work out the colored part of each small square.
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Hint 2 of 2
Add up the colored squares and triangles and compare with the area of the whole figure.
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Approach: add the colored pieces and compare to the whole
- Each small square is one quarter of the whole, and the colored squares and triangles together fill exactly half of the big square.
- Counting the shaded unit squares and the shaded half-squares (triangles) gives a colored area equal to two of the four small squares.
- That is 2 out of 4, i.e. 1/2 of the original square — choice B.
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