VTMO 2026 - Grade 5 - Semifinal - SET 5 - Self-study Question 23

In parallelogram $ABCD$, point $I$ lies on $AD$, and $IC$ meets $BD$ at $K$. Given $S_{\triangle AIB}=15\text{ cm}^2$ and $S_{\triangle BKC}=20\text{ cm}^2$, find the area of $ABCD$ in square centimetres.