2025 AMC 8 Problem 1
Below is the video solution and professionally curated solution for Problem 1 of the 2025 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2025 AMC 8 solutions, or check the answer key.
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Difficulty rating: 720
1.
The eight-pointed star, shown in the figure below, is a popular quilting pattern. What percent of the entire -by- grid is covered by the star?
Video solution:
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Written solution:
There is symmetry, and so whatever fraction of the top-left quarter is shaded, is the same as the fraction of the entire square that is shaded.
Focus on the top-left quarter. Consider moving a single triangle. The shaded area in the problem is exactly the same as the shaded area in this diagram (and the top-left quarter is outlined in bold):
But then it is obvious that exactly half of the top-left quarter is shaded, and so the answer is which is choice B.
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