To find the lateral surface area of the triangular prism, we need to calculate the areas of the three rectangular faces that connect the triangular bases.
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Identifying the triangles:
- The center triangle's base is 12 cm, with heights of its corresponding rectangles being the heights of the connected triangles. The areas are:
- Base = 12 cm, Height = 7.8 cm (one triangle).
- Base = 10 cm, Height = 8 cm (two triangles).
- The center triangle's base is 12 cm, with heights of its corresponding rectangles being the heights of the connected triangles. The areas are:
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Calculating the areas of the rectangular faces:
- The area of the rectangle corresponding to the base of the first triangle (12 cm) and height (7.8 cm): \[ \text{Area}_1 = \text{Base} \times \text{Height} = 12 , \text{cm} \times 7.8 , \text{cm} = 93.6 , \text{cm}^2 \]
- The area of the rectangles corresponding to the two triangles (10 cm each, height 8 cm): \[ \text{Area}2 = 10 , \text{cm} \times 8 , \text{cm} = 80 , \text{cm}^2 \quad \text{(for one)} \] Since there are two of these: \[ \text{Total Area}{2} = 80 , \text{cm}^2 \times 2 = 160 , \text{cm}^2 \]
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Adding the areas together:
- The total lateral surface area is: \[ \text{Lateral Surface Area} = \text{Area}1 + \text{Total Area}{2} = 93.6 , \text{cm}^2 + 160 , \text{cm}^2 = 253.6 , \text{cm}^2 \]
Therefore, the lateral surface area of the triangular prism is 253.6 cm². The correct response is:
253.6 cm².