Question

find the area and perimeter of the rectangle with vertices (1, -2), (-3, -2), (-3, 7), and (1, 7). note that you can draw in the scratch area below, but it is not part of the answer. perimeter: units area: square units

Explanation:

Step1: Find the length and width of the rectangle

The length of the rectangle can be found by calculating the difference in the x - coordinates of two adjacent vertices. Let's take the vertices \((1,-2)\) and \((-3,-2)\). The length \(l\) is \(|1 - (-3)|=4\). The width \(w\) can be found by calculating the difference in the y - coordinates of two adjacent vertices. Let's take the vertices \((-3,-2)\) and \((-3,7)\). The width \(w = |7-(-2)| = 9\).

Step2: Calculate the area of the rectangle

The formula for the area \(A\) of a rectangle is \(A=l\times w\). Substituting \(l = 4\) and \(w = 9\), we get \(A=4\times9 = 36\) square units.

Step3: Calculate the perimeter of the rectangle

The formula for the perimeter \(P\) of a rectangle is \(P = 2(l + w)\). Substituting \(l = 4\) and \(w = 9\), we have \(P=2(4 + 9)=2\times13=26\) units.

Answer:

Perimeter: 26 units
Area: 36 square units