To find length and width, you use the distance formula:
[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
For the length, you use the points [tex](-2, 3)[/tex] and [tex](1, 5)[/tex]
[tex]d=\sqrt{(1-(-2))^{2}+(5-3)^{2}}[/tex]
[tex]=\sqrt{3^{2}+2^{2}}[/tex]
[tex]=\sqrt{9+4}[/tex]
[tex]=\sqrt{13}[/tex]
For the width, you use the points [tex](-2, 3)[/tex] and [tex](2, -3)[/tex]
[tex]d=\sqrt{(2-(-2))^{2}+(-3-3)^{2}}[/tex]
[tex]=\sqrt{4^{2}+(-6)^{2}}[/tex]
[tex]=\sqrt{16+36}[/tex]
[tex]=\sqrt{52}[/tex]
[tex]=2\sqrt{13}[/tex]
So we multiply:
[tex]\sqrt{13}*2\sqrt{13}=2*13=26[/tex]
which is the area.
