10. (10 points) In the figure on the right, $ABCD$ is a rectangle, $EF$ is parallel to $BC$, the area of quadrilateral $AECF$ is 17.5, the area of triangle $AFD$ is 20, the area of triangle $BCE$ is 15, and the area of triangle $CDF$ is 12.5. What is the area of triangle $ABE$?
【Analysis】Since: the area of $\triangle A F D$ plus the area of $\triangle B C E$ equals half the area of the rectangle, from this we can find the area of the rectangle, and then find the area of triangle $A B E$.

【Solution】Solution: The area of $\triangle A F D$ + the area of $\triangle B C E$ = half the area of the rectangle = 20 + 15 = 35, so the area of the rectangle = 35 × 2 = 70,

Therefore, the area of $\triangle A B E$ = 70 - 17.5 - 20 - 15 - 12.5 = 5.
Answer: The area of triangle $A B E$ is 5.