18. (10 points) As shown in the figure, the side length of square $A B C D$ is 20 cm, and $E$ and $F$ are the midpoints of $A B$ and $B C$ respectively. What is the area of quadrilateral $B E G F$ in square centimeters?
【Solution】Solution: As shown in the figure: Take the midpoint of $C D$ and connect it to $A$, take the midpoint of $A D$ and connect it to $B$,
the large square is divided into one small square, four small triangles, and four small trapezoids,
and each small triangle and small trapezoid can be combined to form a small square, making a total of 5 small squares, each with an area of $\frac{1}{5}$ of the large square,
and the area of quadrilateral $B E G F$ is the sum of one small triangle and one small trapezoid, which is $\frac{1}{5}$ of the area of the large square,
so $20 \times 20 \times \frac{1}{5}=80$ (square centimeters);
Answer: The area of quadrilateral $B E G F$ is 80 square centimeters.