Problem 6 · 2023 Math Kangaroo
Medium
Geometry & Measurement
perimeterarea
The big rectangle shown is divided into 30 equally big squares. The perimeter of the area shaded in grey is 240 cm. How big is the area of the big rectangle?
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Answer: D — 1920 cm\(^2\)
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Hint 1 of 2
The grey region's boundary is made of edges of the small squares; count how many such edges it has.
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Hint 2 of 2
Find the side of one small square first, then the whole rectangle's area is 30 of those squares.
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Approach: find the unit side from the shaded perimeter, then total area
- The grey region's outline runs along edges of the small squares; tracing it counts 30 such edges.
- So 30·s = 240 cm, meaning each small square has side s = 8 cm.
- The big rectangle is 30 small squares, each of area 8·8 = 64 cm².
- Total area = 30 · 64 = 1920 cm².
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