Question

What is the area of the rectangle?

40 units²

45 units²

50 units²

55 units²

Answer 1

The area is 50 units.

Explanation:

Use the distance formula to find the length and then the width.

Then use this information to plug into the area formula: a= L x W

Answer 2

see the attached figure with letters to better understand the problem

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=√(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=√(20)\ units`

Step 3

Find the area of the rectangle

`A=AB*AD`

we have

`dAB=√(125)\ units`

`dAD=√(20)\ units`

substitute

`A=√(125)*√(20)`

`A=√(2,500)`

`A=50\ units^(2)`

therefore

the answer is the option

`50\ units^(2)`