Question 9
Answer all ten questions and show detailed solutions. Printed time 60 minutes; each question 4 points. Subcriterion allocations are editorial.
In quadrilateral $ABCD$, $AD\parallel BC$ and $AD\perp DC$. The lengths are $AD=3$, $BC=2$. Point E lies between D and C with $DE=3$ and $EC=1$. Lines AE and BD meet at F. Find the exact area of triangle ABF.
In quadrilateral $ABCD$, $AD\parallel BC$ and $AD\perp DC$. The lengths are $AD=3$, $BC=2$. Point E lies between D and C with $DE=3$ and $EC=1$. Lines AE and BD meet at F. Find the exact area of triangle ABF.