To determine the surface area of a triangular prism, you need to know both the area of the triangular base and the area of the three rectangular faces that connect the corresponding sides of the triangle.
Based on the numbers provided (10, 10, 8, 10, 6), let’s assume they represent the following:
- The triangle has sides measuring \(10\), \(10\), and \(8\) cm (let's pick these as the sides of the triangular face).
- The height of the triangular prism (along the length of the prism) is \(10\) cm.
- The base perpendicular to the height could be \(6\) cm, but for this calculation, we assume it isn't factored as we are getting the area of the prism faces based on the triangular base.
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Calculate the area of the triangular base: Use Heron's formula given the sides of the triangle are \(10\), \(10\), and \(8\).
- \(s = \frac{10 + 10 + 8}{2} = 14\)
- Area \(A\): \[ A = \sqrt{s(s-a)(s-b)(s-c)} = \sqrt{14(14-10)(14-10)(14-8)} \] \[ A = \sqrt{14 \cdot 4 \cdot 4 \cdot 6} = \sqrt{14 \cdot 96} = \sqrt{1344} \approx 36.66 \text{ cm}^2 \]
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Calculate the area of the three rectangular faces:
- The sides measuring \(10\) cm (2 faces): \(10 \times 10 = 100 \text{ cm}^2\) (for both; so \(2 \times 100 = 200\) cm² total).
- The side measuring \(8\) cm: \(8 \times 10 = 80 \text{ cm}^2\).
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Total surface area:
- Add the areas together: \[ \text{Total Surface Area} = 2 \times A + \text{Area of Rectangles} \] \[ \text{Total Surface Area} = 2 \times 36.66 + (200 + 80) = 73.32 + 280 \approx 353.32 \text{ cm}^2 \]
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Possible choices provided do not reflect the calculated area or a possible misinterpretation of the dimensions.
Since the listed responses don't match our calculated surface area result, please clarify the values for a more accurate calculation or check if different dimensions apply. The visible choices may be theoretical options rather than calculated based on provided numbers.
The answer is not directly calculable with provided data directly leading to the options listed but rounding options are substantially higher than those provided (approx 353.32 cm²).
Would you like to adjust or confirm the numbers so we can arrive at one of the listed options?