Problem 6 · 2000 AMC 8
Medium
Geometry & Measurement
area-decomposition
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Answer: A — 7.
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Hint 1 of 2
An L-shape is awkward to measure directly — but it's just a big square with bites taken out. Find the big square's side, then subtract the white bites.
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Hint 2 of 2
The big square's side isn't labeled directly: read it off the top edge as 1 + 4 = 5. Then it's whole-minus-holes.
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Approach: fill in the big square, then subtract the white holes
- The outer square's side isn't given alone, but the top edge reads 1 + 4 = 5, so the square is 5 × 5 = 25.
- The white (non-shaded) pieces are the top 1×1 square, the bottom-right 1×1 square, and the big 4×4 square: 1 + 1 + 16 = 18.
- Shaded L = 25 − 18 = 7.
- You'll see it again: for any L, staircase, or 'frame' region, don't chop it into thin strips — complete it to a full rectangle and subtract the missing rectangles. Far fewer chances to slip.
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