Question

find the perimeter and area of the rectangle with vertices (0, 4), (-4, 4), (-4, -1), and (0, -1). 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: \square units area: \square square units

Explanation:

Step1: Find the length and width

For a rectangle with vertices \((0, 4)\), \((-4, 4)\), \((-4, -1)\), and \((0, -1)\):

• The length (horizontal side) can be found by the difference in the \(x\)-coordinates of \((0, 4)\) and \((-4, 4)\). Using the distance formula for horizontal line (\(y\)-coordinate same), length \(l=\vert0 - (-4)\vert = 4\).
• The width (vertical side) can be found by the difference in the \(y\)-coordinates of \((0, 4)\) and \((0, -1)\). Using the distance formula for vertical line (\(x\)-coordinate same), width \(w=\vert4 - (-1)\vert = 5\).

Step2: Calculate the perimeter

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

Step3: Calculate the area

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

Answer:

Perimeter: \(18\) units
Area: \(20\) square units