Problem 4 · 2023 Math Kangaroo
Medium
Geometry & Measurement
areaarea-decomposition
A small square with side length 4 cm is drawn within a big square with side length 10 cm; their sides are parallel to each other (see diagram). What percentage of the figure is shaded?
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Answer: D — 42 %
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Hint 1 of 2
The shaded parts are the top and bottom trapezoids between the two squares.
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Hint 2 of 2
Each trapezoid has parallel sides 10 and 4; find its height from the leftover border.
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Approach: area of two trapezoids as a fraction of the big square
- The big square has area 10·10 = 100 cm².
- The shaded top and bottom pieces are trapezoids with parallel sides 10 and 4 and height (10−4)/2 = 3.
- Each trapezoid area = (10+4)/2 · 3 = 21 cm², so two of them give 42 cm².
- That is 42/100 = 42% of the figure.
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