Problem 15 · 2024 Math Kangaroo
Stretch
Geometry & Measurement
areasubstitution
The picture shows four rectangles that touch each other. What is the area of the rectangle with the question mark?
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Answer: E — 20 cm²
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Hint 1 of 3
When you know a rectangle's area and one of its sides, divide to get the other side — that unlocks the first missing length.
Still stuck? Show hint 2 →
Hint 2 of 3
Chase the side lengths around the picture, using the overall 13 cm and 16 cm measurements to fill in each missing length in turn.
Still stuck? Show hint 3 →
Hint 3 of 3
Keep going until you know both sides of the question-mark rectangle, then multiply them.
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Approach: recover side lengths from the labelled areas and overall dimensions
- The 5 cm wide rectangle has area 45 cm², so its height is 9 cm; the 13 cm overall height then leaves 4 cm for the strip below it.
- Using the 40 cm² and 48 cm² areas with the 16 cm total width, the remaining side lengths around the question-mark rectangle are forced.
- The question-mark rectangle turns out to be 5 cm by 4 cm.
- Its area is 5 × 4 = 20 cm².
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