2010 AMC 8 Problem 17
Attempt Problem 17 of the 2010 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 2010 AMC 8 solutions, or check the answer key.
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17.
The diagram shows an octagon consisting of unit squares. The portion below is a unit square and a triangle with base If bisects the area of the octagon, what is the ratio
Answer: D
Small hint:
Below , subtract the unit square to get a triangle area equation.
Big hint:
The line cuts the octagon into two equal areas.
Solution:
Since bisects the area, the area under the line is Removing the square on the right makes the bottom a triangle of base with area Let the base of this triangle be
The area being means
Therefore, and This would make
Thus, the answer is D .
Problem 17 in other years
- 1985 AMC 8
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