Triangle in Rectangle
For the original question:
(i) Move the slider to make ABCD a square.
(ii) Change the position of F, what can you observe?
For modification 1:
(i) Move the slider to make AB=5.
(ii) Change the position of F, what can you observe for the area of triangle AEF?
For modification 3:
(i) Move point E such that EF+FC=5. What can you observe?