we are asked to determine the area of the following figure:
we have divided the figure into a rectangle and a triangle. The total area is the sum of the areas of both figures. First, we will find the area of the rectangle:
[tex]\begin{gathered} A_1=(7in)(11in) \\ A_1=77in^2 \end{gathered}[/tex]Now we will find the area of the triangle using the following formula:
[tex]A_2=\frac{bh}{2}[/tex]Where "b" is the base and "h" is the height. The base is found by subtracting the dimension on top to the dimension of the bottom:
[tex]b=15in-11in=4in[/tex]Now we will use the formula:
[tex]A_2=\frac{(4in)(7in)}{2}[/tex]Solving the operations:
[tex]A_2=14in^2[/tex]Now we add both areas:
[tex]\begin{gathered} A=A_1+A_2 \\ A=77in^2+14in^2 \\ A=91in^2 \end{gathered}[/tex]Therefore, the area of the figure is 91 square inches.
