Problem 11 · 2024 AMC 8
Medium
Geometry & Measurement
area
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Answer: D — y = 11.
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Hint 1 of 2
You get to CHOOSE which side is the base. A and B share the same height (y = 7), so AB is horizontal — pick that one and the height becomes trivial.
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Hint 2 of 2
Technique: with a horizontal base, the height is just the vertical gap. Base AB = 6 (from x = 5 to 11); height from C is y − 7.
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Approach: use the horizontal side as the base
- A and B both sit at y = 7, so AB is a flat horizontal segment — the easiest possible base. Its length is just the x-gap: 11 − 5 = 6.
- Because the base is horizontal, the height is simply how far C rises above the line y = 7, namely y − 7 — no distance formula needed. Area = 12 · 6 · (y − 7) = 12.
- So 12 · 6 = 3 times the height equals 12 → height = 4 → y = 7 + 4 = 11. This transfers: on the coordinate plane, always make the base horizontal or vertical — then base and height are just coordinate differences.
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