Question

find the area and perimeter of the rectangle with vertices (5, -1),(5, -5),(-3, -5), and (-3, -1). note that you can draw in the scratch area below, but it is not part of the answer.

Explanation:

Step1: Find the length of the sides

Use the distance formula for two - points $(x_1,y_1)$ and $(x_2,y_2)$ which is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.
For the horizontal side, consider the points $(5,-1)$ and $(-3,-1)$.
$d_1=\sqrt{(-3 - 5)^2+(-1+1)^2}=\sqrt{(-8)^2+0^2}=8$.
For the vertical side, consider the points $(5,-1)$ and $(5,-5)$.
$d_2=\sqrt{(5 - 5)^2+(-5 + 1)^2}=\sqrt{0^2+(-4)^2}=4$.

Step2: Calculate the area

The area formula of a rectangle is $A=l\times w$. Here $l = 8$ and $w = 4$.
$A=8\times4 = 32$.

Step3: Calculate the perimeter

The perimeter formula of a rectangle is $P=2(l + w)$.
$P=2(8 + 4)=2\times12 = 24$.

Answer:

Area: 32 square units
Perimeter: 24 units