To find the surface area of the rectangular prism represented by the net, we can use the areas of the rectangles provided.
We have:
- Two rectangles with measurements 15 inches by 12 inches.
- Two rectangles with measurements 12 inches by 6 inches.
- Two rectangles with measurements 15 inches by 6 inches.
Now, we can calculate the area of each set of rectangles:
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Area of the 15 inches by 12 inches rectangles: \[ \text{Area} = 15 \times 12 = 180 \text{ square inches (for one rectangle)} \] Since there are two of these rectangles, the total area is: \[ 2 \times 180 = 360 \text{ square inches} \]
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Area of the 12 inches by 6 inches rectangles: \[ \text{Area} = 12 \times 6 = 72 \text{ square inches (for one rectangle)} \] Since there are two of these rectangles, the total area is: \[ 2 \times 72 = 144 \text{ square inches} \]
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Area of the 15 inches by 6 inches rectangles: \[ \text{Area} = 15 \times 6 = 90 \text{ square inches (for one rectangle)} \] Since there are two of these rectangles, the total area is: \[ 2 \times 90 = 180 \text{ square inches} \]
Now, we can add the areas of all the rectangles to find the total surface area of the rectangular prism:
\[ \text{Total Surface Area} = 360 + 144 + 180 = 684 \text{ square inches} \]
Thus, the surface area of the rectangular prism is: \[ \boxed{684 \text{ in.}^2} \]