Q:

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]