Question

find the area of the figure below.

Explanation:

Step1: Divide the figure

The figure can be divided into a rectangle and a triangle.

Step2: Calculate the dimensions of the rectangle

The length of the rectangle is the distance between $x = - 7$ and $x = 4$, so $l=4-(-7)=11$. The width of the rectangle is the distance between $y = 1$ and $y=-7$, so $w = 1-(-7)=8$. The area of the rectangle $A_{r}=l\times w=11\times8 = 88$.

Step3: Calculate the dimensions of the triangle

The base of the triangle is the distance between $x=-7$ and $x = 4$, so $b = 11$. The height of the triangle is the distance between $y = 5$ and $y = 1$, so $h=5 - 1=4$. The area of the triangle $A_{t}=\frac{1}{2}\times b\times h=\frac{1}{2}\times11\times4=22$.

Step4: Calculate the total area

The total area of the figure $A=A_{r}+A_{t}=88 + 22=110$.

Answer:

110