Problem 17 · 2018 Math Kangaroo
Stretch
Geometry & Measurement
areaarea-decomposition
The big rectangle is made up of several squares of different sizes. Each of the three smallest squares has area 1. What is the area of the big rectangle?
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Answer: C — 77
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Hint 1 of 3
Each tiny square has area 1, so its side is just 1 little step — use that step as your ruler for everything else.
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Hint 2 of 3
The three tiny squares sit in a row, so the square resting on top of them is 3 steps wide, and you can keep measuring the bigger squares the same way.
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Hint 3 of 3
Once you know how many steps wide and how many steps tall the whole rectangle is, multiply those two numbers.
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Approach: use the side of a tiny square as a measuring step, find each bigger square's side, then multiply the rectangle's width by its height
- Each smallest square has area 1, so its side is 1 step long; the three of them in a row make the bottom-left part 3 steps wide.
- The square sitting on top of those three is 3 steps on each side, and together with the row of tiny squares the left part is 3 + 1 = 4 steps tall; the square next to it is 4 steps on each side, so the bottom strip is 3 + 4 = 7 steps wide.
- The big square on top is as wide as the whole strip, 7 steps, so the rectangle is 7 steps wide and 4 + 7 = 11 steps tall, giving an area of 7 × 11 = 77, answer C.
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