To find the surface area of the triangular prism represented by the net, we need to consider the areas of the different components of the net:
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Area of the three parallelograms: Each parallelogram has a width of 4 cm and a length of 12 cm. The area of one parallelogram is calculated as: \[ \text{Area of one parallelogram} = \text{Width} \times \text{Length} = 4 , \text{cm} \times 12 , \text{cm} = 48 , \text{cm}^2 \] Since there are three parallelograms: \[ \text{Total area of parallelograms} = 3 \times 48 , \text{cm}^2 = 144 , \text{cm}^2 \]
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Area of the two triangular bases: Each right triangle has base and height measuring 9 cm (height) and 12 cm (base). The area of one triangle is calculated as: \[ \text{Area of one triangle} = \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 12 , \text{cm} \times 9 , \text{cm} = \frac{1}{2} \times 108 , \text{cm}^2 = 54 , \text{cm}^2 \] Therefore, the total area of the two triangles is: \[ \text{Total area of triangles} = 2 \times 54 , \text{cm}^2 = 108 , \text{cm}^2 \]
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Total surface area of the triangular prism: To find the total surface area, we add the area of the parallelograms and the area of the triangles: \[ \text{Total Surface Area} = \text{Area of parallelograms} + \text{Area of triangles} = 144 , \text{cm}^2 + 108 , \text{cm}^2 = 252 , \text{cm}^2 \]
Thus, the surface area of the triangular prism is 252 cm².
The correct response is: 252 cm²