Question

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find the area and perimeter 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)

Explanation:

Step1: Find the length and width

The length of the rectangle is the distance between \(x = 5\) and \(x=-3\). Using the formula \(d=\vert x_2 - x_1\vert\), \(l=\vert5-(-3)\vert=\vert5 + 3\vert=8\).
The width of the rectangle is the distance between \(y=-1\) and \(y = - 5\). Using the formula \(d=\vert y_2 - y_1\vert\), \(w=\vert-1-(-5)\vert=\vert-1 + 5\vert=4\).

Step2: Calculate the area

The area formula of a rectangle is \(A=l\times w\). Substitute \(l = 8\) and \(w = 4\) into the formula: \(A=8\times4=32\).

Step3: Calculate the perimeter

The perimeter formula of a rectangle is \(P=2(l + w)\). Substitute \(l = 8\) and \(w = 4\) into the formula: \(P=2(8 + 4)=2\times12 = 24\).

Answer:

Area: \(32\) square units; Perimeter: \(24\) units