Start writing an expression for the area of 3 figures.
[tex]\begin{gathered} square: \\ A=s^2 \\ rectangle: \\ A=l\ast w \\ triangle: \\ A=b\ast\frac{h}{2} \end{gathered}[/tex]Then, write the expression for the shaded region which is the subtraction of the square area with the rectangle and triangle area,
[tex]A_s=s^2-l\ast w-b\ast\frac{h}{2}[/tex]Replace with the given values:
[tex]A_s=(12in)^2-(4in)\ast(3in)-(3in)\ast\frac{(4in)}{2}[/tex]simplify the expression,
[tex]\begin{gathered} A_s=144in^2-12in^2-6in^2 \\ A_s=126in^2 \end{gathered}[/tex]Answer:
The shaded region area is 126in²