Problem 2 · 2019 AMC 8
Medium
Geometry & Measurement
areaarea-decomposition
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Answer: E — 150 square feet.
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Hint 1 of 2
You're only told the short side is 5 — the long side is hidden. Look for a place in the picture where short sides line up against a long side; that shared edge tells you the long side for free.
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Hint 2 of 2
Two short sides stacked equal one long side standing beside them: long = 2 × short. That's the key equation; everything else is one multiplication.
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Approach: let the shared seam set the unknown long side
- Each small rectangle has short side 5. In the picture two rectangles lie stacked on the left while one stands upright on the right — their edges share the same height. Two stacked shorts equal one standing long, so the long side = 2 × 5 = 10.
- Now the big rectangle ABCD has height 10 and width 10 + 5 = 15, so area = 15 × 10 = 150 square feet.
- Why this transfers: in "identical pieces tiled together" figures, a single missing length is almost always pinned by a seam where one orientation lines up flush against another — hunt for that matched edge before reaching for algebra.
Another way — count small rectangles:
- Each small rectangle is 5 by 10, area 50. Three identical pieces tile ABCD with no gaps, so the total is 3 × 50 = 150 square feet — a quick check that matches the 15 × 10 answer.
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