10. (10 points) The area of rectangle $A B C D$ is 70 square centimeters. The vertex $F$ of trapezoid $A F G E$ is on $B C$, and $D$ is the midpoint of the non-parallel side $E G$. Find the area of trapezoid $A F G E$.


【Analysis】According to the problem, connect $D F$. Triangle $A D F$ and rectangle $A B C D$ have the same base and height, so it is known that the area of triangle $A D F$ is half the area of rectangle $A B C D$. Since point $D$ is the midpoint of $E G$, and $A E$ is parallel to $F G$, triangle $A D F$ is also half the area of trapezoid $A F G E$. Because point $D$ is the midpoint of line segment $E G$, the areas of triangle $A D E$ and triangle $D G F$ are half the area of trapezoid $A F G E$, meaning the area of the trapezoid equals the area of the rectangle. According to this, solve the problem.
【Solution】Solution: Triangle $A D F = 70 \div 2 = 35$ (square centimeters),
Since point $D$ is the midpoint of $E G$,
Triangle $A E D +$ Triangle $D F G = 35$ (square centimeters),
The area of trapezoid $A F G E$: $35 + 35 = 70$ (square centimeters),
Answer: The area of trapezoid $A F G E$ is 70 square centimeters.