Problem 18 · 2019 Math Kangaroo
Hard
Geometry & Measurement
areasymmetry
Mia draws some congruent rectangles and one triangle. She then shades grey the parts of the rectangles that lie outside the triangle (see diagram). How big is the resulting grey area?
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Answer: B — 12 cm²
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Hint 1 of 2
Compare the grey parts sticking out with the empty parts of the triangle the rectangles miss.
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Hint 2 of 2
By symmetry those two kinds of regions have equal total area.
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Approach: pair grey overflow with the triangle's uncovered gaps
- The triangle has area ½ × 10 × 6 = 30 cm².
- By the left-right symmetry of the staircase, each grey piece outside the triangle matches an equal empty piece of the triangle not covered by a rectangle.
- Working through the matching, the grey total comes out to 12 cm².
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