ANSWER
[tex]34 {units}^{2} [/tex]
EXPLANATION
The width of the rectangle is |AB|
A(-1,4) and B(3,3)
We use the distance formula,
[tex]d = \sqrt{ {(x_2-x_1)}^{2} + {(y_2-y_1)}^{2} } [/tex]
This implies that,.
[tex]d = \sqrt{ {(3- - 1)}^{2} + {(3 - 4)}^{2} } [/tex]
[tex]d = \sqrt{ {(4)}^{2} + {( - 1)}^{2} } [/tex]
[tex]d = \sqrt{ 16+ 1 } [/tex]
[tex]d = \sqrt{17} [/tex]
The length is BC
C(1,-5) and B(3,3)
[tex]d = \sqrt{ {(3- 1)}^{2} + {(3 - - 5)}^{2} } [/tex]
[tex]d = \sqrt{ {2}^{2} + {(8)}^{2} } [/tex]
[tex]d = \sqrt{4 + 64 } [/tex]
[tex]d = \sqrt{68} [/tex]
[tex]d = 2 \sqrt{17} [/tex]
The area is
[tex] = l \times w[/tex]
[tex] = 2 \sqrt{17} \times \sqrt{17} [/tex]
[tex]2 \times 17 = 34 {units}^{2} [/tex]
