Problem 15 · 2012 Math Kangaroo
Medium
Geometry & Measurement
perimeterarea
The figure on the right has a perimeter of 42 cm. The figure was made from eight equally sized squares. What is the area of the figure?
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Answer: D — 72 cm²
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Hint 1 of 2
The whole boundary is made of equal little square-sides; count how many of them go around.
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Hint 2 of 2
Find one square's side from the perimeter, then the area is 8 of those squares.
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Approach: find the unit side from the perimeter, then total area
- The outline of the figure is made of 14 equal square-edges, so 14 x (side) = 42 cm.
- That gives one side = 42 / 14 = 3 cm.
- Each small square has area 3 x 3 = 9 cm², and there are 8 of them: 8 x 9 = 72 cm².
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