Problem 61090. Covering a 4-pointed star polygon by a circle sector

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 circle that covers the greater of the two distances between opposite vertices (cf. figure below).
Given (A,h), find
  • the width, L, of the rectangle;
  • the angle, α [in Radians], of the sector of the circle such that its area is equal to A;
  • the minimum slicing number n, corresponding to the number of congruent circle slices, such that the area of one slice does not exceed the above sector area.
input: (A, h)
output: y = [L alpha n]
Covering by sector
Solve

Solution Stats

71.43% Correct | 28.57% Incorrect
Last Solution submitted on Dec 06, 2025

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