【Question 14】
In parallelogram $A B C D$, $E F / / A B, H G / / A D$. If the area of parallelogram $A H P E$ is 5 square centimeters, and the area of parallelogram $P E C G$ is 16 square centimeters, then the area of triangle $P B D$ is $\qquad$ square centimeters.
【Analysis and Solution】
According to the half model, $S_{\triangle P D G}=S_{\triangle P B F}, S_{\triangle P D E}=S_{\triangle P B H}, S_{\triangle B C D}=S_{\triangle B A D}$;
$$
\begin{array}{l}
S_{\text {parallelogram } P E C G}-S_{\text {parallelogram } A H P E}=\left(S_{\text {parallelogram } P E C G}+S_{\triangle P D G}+S_{\triangle P B F}\right)-\left(S_{\text {parallelogram } A H P E}+S_{\triangle P D E}+S_{\triangle P B H}\right) \\
=S_{\text {quadrilateral } P B C D}-S_{\text {quadrilateral } P B A D}=\left(S_{\triangle B C D}+S_{\triangle P B D}\right)-\left(S_{\triangle B A D}+S_{\triangle P B D}\right)=S_{\triangle P B D} \times 2 ; \\
S_{\triangle P B D}=\left(S_{\text {parallelogram } P E C G}-S_{\text {parallelogram } A H P E}\right) \div 2=(16-5) \div 2=5.5 \text { square centimeters. }
\end{array}
$$