Given:
The figure is given.
To find:
The area of the figure.
Explanation:
Let us find the area top rectangle.
The length of the rectangle is 4 in.
The breadth of the rectangle is 9 in.
Using the area formula of the rectangle,
[tex]\begin{gathered} A=lb \\ =4\times9 \\ A=36in^2 \end{gathered}[/tex]
Now, let us find the area of the middle rectangle.
The length of the rectangle is 8 in.
The breadth of the rectangle is 6 in.
Using the area formula of the rectangle,
[tex]\begin{gathered} A=lb \\ =8\times6 \\ A=48in^2 \end{gathered}[/tex]
Now, let us find the area of the triangle.
The base is 9 in.
The height is 16 in.
Using the area formula of the triangle,
[tex]\begin{gathered} A=\frac{1}{2}bh \\ =\frac{1}{2}\times9\times16 \\ A=72in^2 \end{gathered}[/tex]
Therefore, the area of the shaded region is,
[tex]\begin{gathered} A=36+48+72 \\ A=156in^2 \end{gathered}[/tex]
Final answer:
The area of the shaded region is 156 square inches.
