Question

find the perimeter and area of the rectangle with vertices (-3, 0), (1, 0), (1, -5), and (-3, -5). 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 of the rectangle can be found by calculating the distance between two points with the same y - coordinate. Let's take the points (-3,0) and (1,0). Using the distance formula for two points \((x_1,y_1)\) and \((x_2,y_2)\) which is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), when \(y_1 = y_2=0\), \(d=\vert x_2 - x_1\vert=\vert1-(-3)\vert = 4\).

Step2: Find the width of the rectangle

The width of the rectangle can be found by calculating the distance between two points with the same x - coordinate. Let's take the points (1,0) and (1, - 5). Using the distance formula, when \(x_1=x_2 = 1\), \(d=\vert y_2 - y_1\vert=\vert-5 - 0\vert=5\).

Step3: Calculate the perimeter

The perimeter \(P\) of a rectangle is given by the formula \(P = 2(l + w)\), where \(l\) is the length and \(w\) is the width. Substituting \(l = 4\) and \(w = 5\), we get \(P=2(4 + 5)=18\).

Step4: Calculate the area

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

Answer:

Perimeter: 18 units
Area: 20 square units