What is the area of the rectangle?40 units²45 units²50 units²55 units²
Accepted Solution
A:
see the attached figure with letters to better understand the problemwe know thatIf the figure is a rectangle then[tex]AB=CD \\AD=BC[/tex]
The area of the rectangle is equal to
[tex]A=B*h[/tex] where B is the base h is the height the base B is equal to the distance AB
the height h is equal to the distance AD Step 1
Find the distance AB
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
[tex]A(-5,5)\\B(0,-5)[/tex] substitute the values
[tex]d=\sqrt{(-5-5)^{2}+(0+5)^{2}}[/tex]
[tex]d=\sqrt{(-10)^{2}+(5)^{2}}[/tex]
[tex]dAB=\sqrt{125}\ units[/tex]
Step 2Find the distance AD
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
[tex]A(-5,5)\\D(-1,7)[/tex] substitute the values
[tex]d=\sqrt{(7-5)^{2}+(-1+5)^{2}}[/tex]
[tex]d=\sqrt{(2)^{2}+(4)^{2}}[/tex]
[tex]dAD=\sqrt{20}\ units[/tex]
Step 3Find the area of the rectangle[tex]A=AB*AD[/tex]we have[tex]dAB=\sqrt{125}\ units[/tex]
[tex]dAD=\sqrt{20}\ units[/tex]
substitute[tex]A=\sqrt{125}*\sqrt{20}[/tex][tex]A=\sqrt{2,500}[/tex][tex]A=50\ units^{2}[/tex]thereforethe answer is the option[tex]50\ units^{2}[/tex]