To find the surface area of the triangular prism, we need to calculate the area of the two triangular bases and the three rectangular faces.
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Area of the triangular base: The base of the triangle can be represented using the formula for the area of a triangle: \[ A = \frac{1}{2} \times \text{base} \times \text{height} \] In this case, the base = 5 inches and the height = 1.5 inches, so: \[ A = \frac{1}{2} \times 5 \text{ in} \times 1.5 \text{ in} = \frac{1}{2} \times 7.5 \text{ in}^2 = 3.75 \text{ in}^2 \] Since there are two triangular bases, the total area of both bases is: \[ 2 \times 3.75 \text{ in}^2 = 7.5 \text{ in}^2 \]
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Area of the rectangular faces: The prism has three rectangular faces, corresponding to each side of the triangular base.
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Rectangular face corresponding to the base (5 in): \[ A_1 = \text{length} \times \text{height} = 5 \text{ in} \times 1.5 \text{ in} = 7.5 \text{ in}^2 \]
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Rectangular face corresponding to the height (1.5 in): \[ A_2 = \text{length} \times \text{height} = 1.5 \text{ in} \times 1.5 \text{ in} = 2.25 \text{ in}^2 \]
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Rectangular face corresponding to the hypotenuse (5.22 in): \[ A_3 = \text{length} \times \text{height} = 5.22 \text{ in} \times 1.5 \text{ in} = 7.83 \text{ in}^2 \]
Now, we can add the areas of the rectangular faces: \[ A_{rect} = A_1 + A_2 + A_3 = 7.5 \text{ in}^2 + 2.25 \text{ in}^2 + 7.83 \text{ in}^2 = 17.58 \text{ in}^2 \]
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Total surface area: Now, combine the total area of the bases and the area of the rectangular faces: \[ \text{Total Surface Area} = \text{Area of bases} + \text{Area of rectangular faces} = 7.5 \text{ in}^2 + 17.58 \text{ in}^2 = 25.08 \text{ in}^2 \]
So, the surface area of the prism is 25.08 in². The correct response is: 25.08 in.².