Problem 61091. Slicing a 4-pointed star polygon

Given the area, A, of a 4-pointed star polygon formed by the rectangle, with dimensions L×2L, and four triangles, with height h from their bases to the vertices, consider the area, A_r, of the circle that covers the shorter of the two distances between opposite vertices (cf. left figure below) and slice the star polygon by 8 slices (cf. right figure below).
Given (A,h), find the 9×2 matrix, M = [A1 a1; A2 a2; ...; A8 a8; A_r/π n], where
  • in the first row (i=1), A1 stands for the area of one 'blue' slice of the 4-pointed star polygon (cf. right figure), and a1 stands for the logical 1 if A1 does not exceed the circle's area, A_r, or a1 stands for the logical 0 otherwise;
  • in the second row (i=2), A2 stands for the area of two slices (cumulative sum of 'blue' and 'green' slices by consecutive vertices), and a2 has the same previous false-true meaning relative to the areas A2 and A_r;
  • and so on, until last slice of the 4-pointed star polygon;
  • in the last row (i=9), A_r is the area of the circle, and n stands for the maximum number of slices that their cumulative area does not exceed the circle area.
Hint: The slices of the 4-pointed star polygon are not congruent among each other.
input: (A, h)
output: M = [A1 a1; A2 a2; ...; A8 a8; A_r/pi n]
Solve

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100.0% Correct | 0.0% Incorrect
Last Solution submitted on Dec 08, 2025

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