Question

What is the area of the rectangle?

Answer 1

Answer:

$50\ units^{2}$

Step-by-step explanation:

Plot the figure to better understand the problem

see the attached figure

we know that

If the figure is a rectangle          

then

$AB=CD \\AD=BC$

The area of the rectangle is equal to

$A=B*h$

 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

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

$A(-5,5)\\B(0,-5)$

substitute the values

$d=\sqrt{(-5-5)^{2}+(0+5)^{2}}\\d=\sqrt{(-10)^{2}+(5)^{2}}\\dAB=\sqrt{125}\ units$

Step 2

Find the distance AD

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

$A(-5,5)\\D(-1,7)$

substitute the values

$d=\sqrt{(7-5)^{2}+(-1+5)^{2}}\\d=\sqrt{(2)^{2}+(4)^{2}}\\dAD=\sqrt{20}\ units$

Step 3

Find the area of the rectangle

$A=AB*AD$

we have

$dAB=\sqrt{125}\ units\\dAD=\sqrt{20}\ units$

substitute

$A=\sqrt{125}*\sqrt{20}\\A=\sqrt{2,500}\\A=50\ units^{2}$