VTMO 2026 - Grade 7 - Semifinal - SET 5 - Self-study Question 21

Equilateral triangle $ABC$ has area $100$ cm$^2$. Point $I$ lies on $BC$ with $IC=4IB$. The line through $I$ perpendicular to $AB$ meets the line $AC$ at $F$. Find the area of triangle $AIF$, in cm$^2$.