The eight-pointed star, shown in the figure below, is a popular quilting pattern. What percent of the entire 4-by-4 grid is covered by the star?

A. 40

B. 50

C. 60

D. 75

E. 80

1. 2025 AMC 8 官方解析

Answer (B): The area of the outer square is $4 \cdot 4 = 16$. The star is made of 8 shaded areas, each of which is a parallelogram. Each parallelogram consists of two isosceles right triangles whose combined area is $1$. Thus the area of the star is $8$, covering exactly half, which is $50\%$, of the entire 4-by-4 grid.

OR

The figure has 4 completely filled squares at the center and 4 completely empty squares at the corners, so half of that area is covered by the star. The remaining 8 squares are each half-filled by an isosceles right triangle. Therefore, the entire star covers half, which is $50\%$, of the entire 4-by-4 grid.