VTMO 2026 - Grade 9 - Semifinal - SET 06 - Self-study Question 17

Three cevians of triangle $ABC$ concur at an interior point $P$, meeting opposite sides at $D,E,F$. As shown, the small areas are $[BPD]=40$, $[DPC]=20$, and $[APE]=15$. Find $[ABC]$.