14. As shown in the figure, in square $A B C D$, the area of square $A M O P$ is 8 square centimeters, and the area of square $C N O Q$ is 24.5 square centimeters. What is the area of square $A B C D$ in square centimeters?
14. As shown in the figure, in square $A B C D$, the area of square $A M O P$ is 8 square centimeters, and the area of square $C N O Q$ is 24.5 square centimeters. What is the area of square $A B C D$ in square centimeters?
【Analysis】Based on the area of square $A M O P$ being 8 square centimeters and the area of square $C N O Q$ being 24.5 square centimeters, we can find the lengths of the diagonals $A O$ and $O C$, which will give us the diagonal of square $A B C D$, allowing us to determine the area of square $A B C D$.
【Solution】In square $A B C D$, the area of square $A M O P$ is 8 square centimeters, so the diagonal $A O$ $=4 \mathrm{~cm}$,
The area of square $C N O Q$ is 24.5 square centimeters, so the diagonal $O C=7 \mathrm{~cm}$,
Therefore, the diagonal of square $A B C D$ is $4+7=11 \mathrm{~cm}$.
Thus, the area of square $A B C D$ is $\frac{1}{2} \times 11^{2}=60.5$ square centimeters.
Answer: The area of square $A B C D$ is 60.5 square centimeters.