Question

plot and connect the points in the order listed below. when you are done, find the area of the resulting figure.
a(-9,0), b(-6,5), c(5,5), d(5,-5), e(-6,-5)

Explanation:

Step1: Analyze the figure

The figure is composed of a parallelogram \(ABEC\) and a rectangle \(CDBE\).

Step2: Calculate the area of the parallelogram

The base of the parallelogram \(ABEC\): The distance between \(A(-9,0)\) and \(B(-6,5)\) in the \(x -\) direction is \(|-6-(-9)| = 3\). The height is \(5\). The area of a parallelogram \(A_{1}=base\times height\). Using the formula \(A_{1}=3\times10 = 30\) (the vertical distance from \(y=- 5\) to \(y = 5\) is \(|5-(-5)|=10\)).

Step3: Calculate the area of the rectangle

The length of the rectangle \(CDBE\): The distance between \(C(5,5)\) and \(B(-6,5)\) is \(|5-(-6)|=11\). The width is \(10\) (vertical distance from \(y=-5\) to \(y = 5\)). The area of a rectangle \(A_{2}=length\times width\), so \(A_{2}=11\times10=110\).

Step4: Calculate the total area

The total area \(A = A_{1}+A_{2}\).

Answer:

\(A=30 + 110=140\)