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 of one right triangle can be calculated using the formula:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
For the triangles given in the problem:
- Base = 3 inches
- Height = 4 inches
Calculating the area of one triangle:
\[ \text{Area} = \frac{1}{2} \times 3 \times 4 = \frac{1}{2} \times 12 = 6 \text{ square inches} \]
Since there are two congruent triangles, the total area of the triangles is:
\[ \text{Total Area of Triangles} = 2 \times 6 = 12 \text{ square inches} \]
Now, we know the total area of the composite shape is 40 square inches. To find the area of the rectangle, we subtract the area of the triangles from the total area:
\[ \text{Area of Rectangle} = \text{Total Area} - \text{Total Area of Triangles} \]
\[ \text{Area of Rectangle} = 40 - 12 = 28 \text{ square inches} \]
Therefore, the area of the rectangle within the composite shape is 28 square inches.
Final Answer: 28 square inches