To find the area of the figure, we can break the shape into two parts: the triangle (Δ) and the rectangle (□). Let's go through each step:

1. Area of the triangle (Δ):

   • The base $b$ of the triangle is 12 inches (the same as the base of the rectangle).
   • The height $h$ of the triangle is 4 inches.
   • The formula for the area of a triangle is:

   $A_\Delta = \frac{1}{2} \times b \times h$

   Substituting the values:

   $A_\Delta = \frac{1}{2} \times 12 \times 4 = 24 \, \text{in}^2$

2. Area of the rectangle (□):

   • The width is 12 inches, and the height is 9 inches.
   • The formula for the area of a rectangle is:

   $A_\Box = \text{width} \times \text{height}$

   Substituting the values:

   $A_\Box = 12 \times 9 = 108 \, \text{in}^2$

3. Total area of the figure:

   • The total area is the sum of the areas of the triangle and the rectangle:

   $A_{\text{total}} = A_\Delta + A_\Box = 24 + 108 = 132 \, \text{in}^2$

Thus, the total area of the figure is $132 \, \text{in}^2$.

Would you like further details or explanations on any step?

Related Questions:

1. How do we calculate the area of a trapezoid if given a different shape?
2. What are the other ways to decompose complex shapes into simpler parts?
3. Can the Pythagorean theorem be used to verify the dimensions of the triangle here?
4. How would the total area change if the height of the triangle was doubled?
5. How does the area formula for a parallelogram differ from that of a rectangle?

Tip:

When working with composite shapes, breaking them into basic shapes (triangles, rectangles, circles) can simplify area calculations.