To find the area of the rectangle within the composite shape, let's first calculate the area of the two congruent right triangles.
The formula for the area of a triangle is: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
Given that the width (base) of each triangle is 3 inches and the height is 4 inches, we can calculate the area of one triangle as follows: \[ \text{Area of one triangle} = \frac{1}{2} \times 3 \times 4 = \frac{1}{2} \times 12 = 6 \text{ square inches} \]
Since there are two congruent triangles, 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 can subtract the area of the triangles from the total area: \[ \text{Area of rectangle} = \text{Total area} - \text{Total area of triangles} \] \[ \text{Area of rectangle} = 40 - 12 = 28 \text{ square inches} \]
Thus, the area of the rectangle within the composite shape is: \[ \boxed{28 \text{ square inches}} \]