2025 AMC 8 Problems/Problem 1
Contents
[hide]Problem
The eight-pointed star, shown in the figure below, is a popular quilting pattern. What percent of the entire
Solution 1
Each of the side triangles has base length and height
, so they all have area
. Each of the four corner squares has side length
and hence area
. Then the area of the shaded region is
. Since
, our answer is
. ~cxsmi
Solution 2
There are total squares in the diagram and each square can have
triangles. Thus, the total number of triangles in the diagram is
triangles. There are
shaded triangles in the diagram (you can just count this up), so the percentage of the shaded triangles is
. ~Pi_in_da_box
Video Solution 1 by SpreadTheMathLove
https://www.youtube.com/watch?v=jTTcscvcQmI
See Also
2025 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by First Problem |
Followed by Problem 2 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.