2002 AMC 8 Problem 20
Attempt Problem 20 of the 2002 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2002 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
20.
The area of triangle is square inches. Points and are midpoints of congruent segments and Altitude bisects The area (in square inches) of the shaded region is
Answer: D
Small hint:
The altitude splits the isosceles triangle into two equal halves.
Big hint:
The segment through the midpoints creates a similar triangle with half the side lengths.
Solution:
Since and bisects altitude splits into two congruent triangles. The left half has area
In point is the midpoint of The horizontal segment through meets halfway up, so the small top triangle is similar to with scale factor Its area is therefore of or
The shaded region is the rest of the left half, so its area is
Thus, D is the correct answer.
Problem 20 in other years
- 1985 AMC 8
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