[tex]A=(-2,3),~~C=(1,-1)\\\\\mid AC \mid = \sqrt{(1-(-2))^{2} +(-1-3)^{2} } =\sqrt{3^{2} +(-4)^{2} } =\sqrt{9+16} =\sqrt{25} =\sqrt{5^{2} } =5\\\\a-dlugosc~~boku~~kwadrata\\a\sqrt{2} -przekatna ~~kwadrata\\\\a\sqrt{2} =\mid AC \mid ~~\land~~\mid AC \mid =5~~\Rightarrow~~a\sqrt{2} =5\\\\a\sqrt{2} =5~~~\mid \div \sqrt{2} \\\\a=\dfrac{5}{\sqrt{2} } \\\\a=\dfrac{5}{\sqrt{2} } \cdot \dfrac{\sqrt{2} }{\sqrt{2} } =\dfrac{5\sqrt{2} }{2} \\\\\\P_{ABCD} =a^{2} ~~\land ~~a=\dfrac{5}{\sqrt{2} } \\\\[/tex]
[tex]P_{ABCD} =(\frac{5}{\sqrt{2} } )^{2} =\frac{5}{\sqrt{2} }\cdot \frac{5}{\sqrt{2} }\\\\P_{ABCD} =\dfrac{25}{2} \\\\P_{ABCD} =12\frac{1}{2} ~~[j^{2} ][/tex]
