解：?$(2)$?過點?$D$?作?$DE//AC$?交?$BC$?的延長線于點?$E，$?如圖
∵?$AD//BC($?已知?$)，$?即?$AD//CE$?
∴四邊形?$ACED$?是平行四邊形
∴?$AC = DE$?
又∵四邊形?$ABCD$?是等腰梯形
∴?$AC = BD$?
∴?$BD = DE$?
∵?$DE//AC，$??$AC⊥BD$?
∴?$∠BDE = ∠BPC = 90°$?
∴?$∠DBC = 45°$?
∴?$PC = PB = 7\ \mathrm {cm}$?
∵?$AD//BC$?
∴?$∠ADP = 45°$?
∴?$PD = PA = 3\ \mathrm {cm}$?
∴?$AC = BD = 7+3 = 10\ \mathrm {cm}$?
∴?$S_{梯形ABCD}= \frac 12AC·BD=\frac 12×10×10= 50(\mathrm {cm}^2)$?
