[tex]P=\frac{(a+b)h}{2}\\\\P=\frac{(2\sqrt{3}+4\sqrt{2})\not2\sqrt{6}}{\not2}\\\\P=(2\sqrt{3}+4\sqrt{2})\sqrt{6}\\P=2\sqrt{3\cdot6}+4\sqrt{2\cdot6}\\P=2\sqrt{18}+4\sqrt{12}\\P=2\cdo\sqrt{9\cdot2}+4\sqrt{4\cdot3}\\P=2\cdot3\sqrt{2}+4\cdot2\sqrt{3}\\P=\boxed{6\sqrt{2}+8\sqrt{3}\,\text{j}^2}[/tex]
