To find the area of the rectangle within the composite shape, we first need to calculate the area of the two congruent right triangles.
Each right triangle has a height of 4 inches and a width of 3 inches. The area \(A\) of a right triangle can be calculated using the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
For one triangle:
\[ A = \frac{1}{2} \times 3 \times 4 = \frac{1}{2} \times 12 = 6 \text{ square inches} \]
Since there are two congruent triangles, the total area 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 given as 40 square inches. Thus, we can find the area of the rectangle by subtracting 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.
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