Answer:
Option 2) 30 square units
Step-by-step explanation:
step 1
Plot the rectangle to better understand the problem
we have
A(1, 2),B(5, 0),C(2, -6) and D(-2, -4)
see that attached figure
step 2
Find the length of the sides
Remember that'
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Find the length side AB
we have
A(1, 2),B(5, 0)
substitute in the formula
[tex]d=\sqrt{(0-2)^{2}+(5-1)^{2}}[/tex]
[tex]d=\sqrt{(-2)^{2}+(4)^{2}}[/tex]
[tex]d_A_B=\sqrt{20}\ units[/tex]
Find the length side BC
we have
B(5, 0),C(2, -6)
substitute in the formula
[tex]d=\sqrt{(-6-0)^{2}+(2-5)^{2}}[/tex]
[tex]d=\sqrt{(-6)^{2}+(-3)^{2}}[/tex]
[tex]d_B_C=\sqrt{45}\ units[/tex]
step 3
Find the area of rectangle
The area of rectangle is equal to
[tex]A=LW[/tex]
we have
[tex]L=BC=\sqrt{45}\ units[/tex]
[tex]W=AB=\sqrt{20}\ units[/tex]
substitute
[tex]A=(\sqrt{45})(\sqrt{20})=\sqrt{900}=30\ units^2[/tex]
