To find the area of the rectangle within the composite figure, first, we need to determine the area of the two congruent right triangles.
The area \( A \) of a right triangle is given by the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
For the triangles in the composite figure:
- Base = width = 3 inches
- Height = 4 inches
Calculating the area of one triangle:
\[ A = \frac{1}{2} \times 3 \times 4 = \frac{12}{2} = 6 \text{ square inches} \]
Since there are two congruent triangles, the total area of both triangles is:
\[ \text{Total area of triangles} = 2 \times 6 = 12 \text{ square inches} \]
Now, we know the total area of the composite figure is 40 square inches. To find the area of the rectangle, we subtract the area of the triangles from the total area of the composite figure:
\[ \text{Area of rectangle} = \text{Total area} - \text{Total area of triangles} \] \[ \text{Area of rectangle} = 40 - 12 = 28 \text{ square inches} \]
Thus, the area of the rectangle within the composite shape is:
28 square inches.