Problem 17 · 2009 Math Kangaroo
Stretch
Geometry & Measurement
areacomplementary-counting
Two rectangles, one measuring 8 × 10 and the other 9 × 12, overlap as shown. The dark grey area is 37. What is the area of the light grey part?
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Answer: E — 65
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Hint 1 of 2
The two rectangles share the same overlap region — give it a name.
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Hint 2 of 2
Dark grey is one rectangle minus the overlap; write light grey the same way and substitute.
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Approach: shared overlap
- Let the overlap area be O. The 8×10 rectangle has area 80, so dark grey = 80 − O = 37, giving O = 43.
- The 9×12 rectangle has area 108, so light grey = 108 − O.
- Light grey = 108 − 43 = 65 — answer E.
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