Problem 10 · 2020 Math Kangaroo
Stretch
Geometry & Measurement
area-fractionarea-decomposition
Martinho made a two-colour kite with six pieces of a thin strip of bamboo. Two pieces were used for the diagonals, which are perpendicular. The other four pieces were used to connect the midpoints of the sides of the kite, as shown in the picture. What is the ratio between the blue and yellow parts of the kite?
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Answer: E — 1
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Hint 1 of 2
Joining the midpoints of any quadrilateral’s sides makes a parallelogram inside it.
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Hint 2 of 2
That midpoint parallelogram always has exactly half the area of the original shape.
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Approach: use the Varignon midpoint-parallelogram half-area fact
- The blue region is the parallelogram formed by the midpoints of the kite’s sides.
- For any quadrilateral, this midpoint parallelogram has half the total area.
- So blue = yellow, and the ratio is 1.
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