HMMT 十一月 2025 · THM 赛 · 第 3 题

HMMT November 2025 — THM Round — Problem 3

Let V EN U S be a convex pentagon with area 84. Given that N V is parallel to SU , SE is parallel to U N , and triangle SU N has area 24, compute the maximum possible area of triangle EU V .

解析

Let V EN U S be a convex pentagon with area 84. Given that N V is parallel to SU , SE is parallel to U N , and triangle SU N has area 24, compute the maximum possible area of triangle EU V . Proposed by: Alan Vladimiroff, David Wei Answer: 36 Solution: U N S E V As SE is parallel to U N , triangles SU N and EU N have the same height from base U N . Therefore, [ EU N ] = [ SU N ] = 24. Similarly, since N V is parallel to SU , triangles SU N and SU V have the same height from base SU . Therefore, [ SU V ] = [ SU N ] = 24. Finally, we compute [ EU V ] = [ V EN U S ] − [ EU N ] − [ SU V ] = 84 − 24 − 24 = 36 .