Answer:
The area of the rectangle is 42 units^2
Step-by-step explanation:
we know that
The area of rectangle is equal to
[tex]A=LW[/tex]
In this problem
AB=DC
BC=AD
see the attached figure with letters to better understand the problem
we have that
[tex]L=BC\\W=AB[/tex]
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have the points
[tex]A(2,-1),B(5,2),C(12,-5),D(9,-8)[/tex]
Find out the distance BC
we have
[tex]B(5,2),C(12,-5)[/tex]
substitute in the formula
[tex]d=\sqrt{(-5-2)^{2}+(12-5)^{2}}[/tex]
[tex]d=\sqrt{(-7)^{2}+(7)^{2}}[/tex]
[tex]d_B_C=\sqrt{98}\ units[/tex]
Find out the distance AB
we have
[tex]A(2,-1),B(5,2)[/tex]
substitute in the formula
[tex]d=\sqrt{(2+1)^{2}+(5-2)^{2}}[/tex]
[tex]d=\sqrt{(3)^{2}+(3)^{2}}[/tex]
[tex]d_A_B=\sqrt{18}\ units[/tex]
Find out the area
[tex]A=(L)(W)[/tex]
we have
[tex]L=d_B_C=\sqrt{98}\ units[/tex]
[tex]W=d_A_B=\sqrt{18}\ units[/tex]
substitute
[tex]A=(\sqrt{98})(\sqrt{18})=42.0\ units^2[/tex]
