[tex]a)~~A_{\square} = l^2 = \Big(2 \sqrt{3}+1 \Big)^2=(2 \sqrt{3})^2 + 2\times 2 \sqrt{3}\times 1 + 1^2= \\
=12 + 4\sqrt{3} + 1 = \boxed{13 + 4\sqrt{3}~cm^2} \\ \\
b)~A_{\boxed{~~}}=L\cdot l=( \sqrt{3} + \sqrt{2})( \sqrt{3} - \sqrt{2})=\sqrt{3}^2 - \sqrt{2}^2 =3-2=\boxed{1~cm^2} \\ \\
c)~~A_{\lozenge}=d_1\cdot d_2=(3 \sqrt{3}+5 )(3 \sqrt{3}-5)=27-25 =\boxed{2~cm^2}\\\displaystyle\\
d)~~A_\Delta = \frac{c_1 \cdot c_2}{2} =\frac{(2 \sqrt{3}+3)(2 \sqrt{3}-3)}{2}=\frac{12-9}{2}= \boxed{\frac{3}{2} ~cm^2}[/tex]
