Problem 61081. Slicing the area of a regular polygon

Given the area, A, of a regular polygon with n sides, each of length s, consider its decomposition in congruent isosceles triangles of base s and heigth h. Find the rectangle, with dimensions L×h, which covers all n triangles in their adjacent positions (n>3, cf. figure below). Complete the problem by determining the area, A_r, of the rectangle.
Hint: Consider that we are slicing the polygon into triangular slices and put them into the rectangle.
input: (A, n)
output: y = [L h A_r]
Slicing square (n=4)
Solve

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87.5% Correct | 12.5% Incorrect
Last Solution submitted on Jan 15, 2026

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