To obtain the area of the composite figure, the following steps are necessary:
Step 1: Recall the formulas for the area of a rectangle and a triangle (since they both make up the composite figure), as given below:
[tex]\begin{gathered} A_{rec\tan gle}=length\text{ }\times width \\ A_{triangle}=\frac{1}{2}\times base\times height \end{gathered}[/tex]
Step 2: Compute the areas of the rectangle and triangle using the formulas above
[tex]\begin{gathered} A_{rec\tan gle}=length\text{ }\times width \\ \Rightarrow A_{rec\tan gle}=7\text{ }\times6=42 \\ A_{triangle}=\frac{1}{2}\times base\times height \\ \Rightarrow A_{triangle}=\frac{1}{2}\times3\times6=\frac{18}{2}=9 \end{gathered}[/tex]
Step 3: Add the two areas together, as follows:
[tex]A_{composite}=A_{rec\tan gle}+A_{triangle}[/tex]
Thus:
[tex]\begin{gathered} A_{composite}=42+9=51 \\ \Rightarrow A_{composite}=51in^2 \end{gathered}[/tex]
Therefore, the area of the composite figure is 51 inches squared (option A)
