Question

find the area and perimeter of the rectangle with vertices (1, - 5), (-3, - 5), (-3, 0), and (1, 0). 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 rectangle

The length can be found by calculating the distance between two points on the same - y - coordinate. Let's take the points \((1,-5)\) and \((-3,-5)\). Using the distance formula for two points \((x_1,y_1)\) and \((x_2,y_2)\) which is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), since \(y_1=y_2=-5\), the length \(l=\vert1-(-3)\vert=\vert1 + 3\vert=4\).

Step2: Find the width of the rectangle

Take the points \((-3,-5)\) and \((-3,0)\). Since \(x_1=x_2=-3\), the width \(w=\vert0-(-5)\vert=\vert0 + 5\vert=5\).

Step3: Calculate the area of the rectangle

The area formula of a rectangle is \(A=l\times w\). Substituting \(l = 4\) and \(w = 5\), we get \(A=4\times5 = 20\).

Step4: Calculate the perimeter of the rectangle

The perimeter formula of a rectangle is \(P=2(l + w)\). Substituting \(l = 4\) and \(w = 5\), we have \(P=2(4 + 5)=2\times9=18\).

Answer:

Area: 20 square units
Perimeter: 18 units