Question

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

Explanation:

Step1: Find the length of the rectangle

The length can be found by calculating the distance between two points with the same y - coordinate. Using the distance formula for two points $(x_1,y)$ and $(x_2,y)$ which is $d=\vert x_1 - x_2\vert$. For points $(5, - 1)$ and $(-3,-1)$, $d_1=\vert5-(-3)\vert=\vert5 + 3\vert=8$.

Step2: Find the width of the rectangle

The width can be found by calculating the distance between two points with the same x - coordinate. Using the distance formula for two points $(x,y_1)$ and $(x,y_2)$ which is $d=\vert y_1 - y_2\vert$. For points $(-3,-1)$ and $(-3,-5)$, $d_2=\vert-1-(-5)\vert=\vert-1 + 5\vert=4$.

Step3: Calculate the perimeter

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

Step4: Calculate the area

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

Answer:

Perimeter: 24 units
Area: 32 square units