Question

find the perimeter and area of the rectangle with vertices (5, 2), (-4, 2), (-4, 7), and (5, 7). 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 and width

For the x - coordinates of the vertices \((5,2)\) and \((- 4,2)\), the distance (length of the horizontal side) is \(|5 - (-4)|=|5 + 4| = 9\). For the y - coordinates of the vertices \((-4,2)\) and \((-4,7)\), the distance (length of the vertical side) is \(|7 - 2|=5\). So the length \(l = 9\) and width \(w = 5\) of the rectangle.

Step2: Calculate the perimeter

The formula for the perimeter \(P\) of a rectangle is \(P=2(l + w)\). Substitute \(l = 9\) and \(w = 5\) into the formula: \(P=2(9 + 5)=2\times14 = 28\).

Step3: Calculate the area

The formula for the area \(A\) of a rectangle is \(A=l\times w\). Substitute \(l = 9\) and \(w = 5\) into the formula: \(A = 9\times5=45\).

Answer:

Perimeter: \(28\) units, Area: \(45\) square units