To find the area of the rectangle within the composite shape, we first need to calculate the area of the two congruent right triangles.
The formula for the area of a triangle is: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
For each triangle, the base is 3 inches and the height is 4 inches: \[ \text{Area of one triangle} = \frac{1}{2} \times 3 \times 4 = \frac{1}{2} \times 12 = 6 \text{ square inches} \] Since there are two congruent triangles: \[ \text{Area of two triangles} = 2 \times 6 = 12 \text{ square inches} \]
Now, we have the total area of the composite figure, which is given as 40 square inches. To find the area of the rectangle, we subtract the area of the triangles from the total area: \[ \text{Area of rectangle} = \text{Total area} - \text{Area of two triangles} \] \[ \text{Area of rectangle} = 40 - 12 = 28 \text{ square inches} \]
Thus, the area of the rectangle within the composite shape is: \[ \boxed{28 \text{ square inches}} \]