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 area of one right triangle is given by the formula:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
In this case, the base of each triangle is 3 inches and the height is 4 inches:
\[ \text{Area} = \frac{1}{2} \times 3 , \text{inches} \times 4 , \text{inches} = \frac{1}{2} \times 12 , \text{square inches} = 6 , \text{square inches} \]
Since there are two congruent triangles, the total area of the two triangles is:
\[ \text{Total area of triangles} = 2 \times 6 , \text{square inches} = 12 , \text{square inches} \]
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:
\[ \text{Area of the rectangle} = \text{Total area} - \text{Area of triangles} = 40 , \text{square inches} - 12 , \text{square inches} = 28 , \text{square inches} \]
So, the area of the rectangle within the composite shape is:
28 square inches.
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