2007 AMC 8 Problem 23
Attempt Problem 23 of the 2007 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 2007 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
23.
What is the area of the shaded pinwheel shown in the grid?
Answer: B
Small hint:
It is easier to subtract the unshaded area from the whole grid.
Big hint:
The unshaded part consists of four corner squares and four congruent triangles.
Solution:
We can find the area of the shaded part by subtracting the area of the unshaded part from the whole area.
There are squares with side length contributing each to the unshaded area, for a total of
There are also triangles with base and height This contributes a total area of
The total unshaded area is therefore
The total area is and subtracting the unshaded area yields as the area of the shaded region.
Thus, B is the correct answer.
Problem 23 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
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- 1989 AMC 8
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