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areas in a regular-hexagon-shaped 2020 BMT Individual 13

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January 6, 2022
areasgeometryhexagon

Problem Statement

Sheila is making a regular-hexagon-shaped sign with side length 1 1. Let ABCDEFABCDEF be the regular hexagon, and let R,S,TR, S,T and U be the midpoints of FAFA, BCBC, CDCD and EFEF, respectively. Sheila splits the hexagon into four regions of equal width: trapezoids ABSRABSR, RSCFRSCF , FCTUFCTU, and UTDEUTDE. She then paints the middle two regions gold. The fraction of the total hexagon that is gold can be written in the form m/nm/n , where m and n are relatively prime positive integers. Compute m+nm + n. https://services.artofproblemsolving.com/download.php?id=YXR0YWNobWVudHMvYS9lLzIwOTVmZmViZjU3OTMzZmRlMzFmMjM1ZWRmM2RkODMyMTA0ZjNlLnBuZw==&rn=MjAyMCBCTVQgSW5kaXZpZHVhbCAxMy5wbmc=
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