To find the area of the rectangle within the composite shape, we first need to determine the area of the two congruent right triangles.
The area \( A \) of one right triangle can be calculated using the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
In this case, the base is 3 inches and the height is 4 inches. Substituting these values into the formula gives:
\[ A = \frac{1}{2} \times 3 \times 4 = \frac{1}{2} \times 12 = 6 \text{ square inches} \]
Since there are two congruent triangles, the total area for both triangles is:
\[ \text{Total area of triangles} = 2 \times 6 = 12 \text{ square inches} \]
Now we know that the total area of the composite figure is 40 square inches. To find the area of the rectangle, we subtract the combined area of the triangles from the total area of the composite figure:
\[ \text{Area of rectangle} = \text{Total area} - \text{Area of triangles} = 40 - 12 = 28 \text{ square inches} \]
Thus, the area of the rectangle within the composite shape is:
28 square inches.