Problem 2 · 2014 Math Kangaroo
Easy
Geometry & Measurement
careful-counting
How many quadrilaterals of any size are there in the diagram?
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Answer: D — 4
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Hint 1 of 2
A quadrilateral is any four-sided shape, not just the two whole rectangles you see drawn.
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Hint 2 of 2
The overlap line splits each rectangle, so look for the smaller rectangles hidden inside as well.
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Approach: list every four-sided region
- Each of the two drawn rectangles is itself a quadrilateral: that is 2.
- Where they overlap, the shared region is a smaller rectangle, a third quadrilateral.
- The edge of one rectangle cuts the other, leaving a fourth rectangular strip beside the overlap.
- Counting all four-sided regions gives 4 quadrilaterals.
Mark:
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