Question

What is the area of the rectangle?

Answer 1

The area of the rectangle is 60 square units.

Explanation:

The given figure represents a rectangle with vertices (-5,2), (-7,-2), (5,-8) and (7,-4).

Distance formula:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

Find the distance between (-5,2) and (7,-4), to calculate the length of the rectangle.

`l=√((7-(-5))^2+(-4-2)^2)=√((12)^2+(-6)^2) =√(144+36)=√(180)`

Find the distance between (7,-4) and (5,-8), to calculate the width of the rectangle.

`w=√((5-7)^2+(-8-(-4))^2)=√((-2)^2+(-4)^2)=√(4+16)=√(20)`

The area of rectangle is

`A=l* w`

`A=√(180)* √(20)`

`A=√(3600)`

`A=60`

Therefore the area of the rectangle is 60 square units.