To find the surface area of the triangular prism, we need to calculate the areas of the two triangular bases and the three rectangular faces.
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Finding the area of the triangular base: The given triangular face has all sides measuring 10 cm, which means it's an equilateral triangle. The area \( A \) of an equilateral triangle can be calculated using the formula:
\[ A = \frac{\sqrt{3}}{4} s^2 \]
where \( s \) is the length of a side. For our triangle:
\[ A = \frac{\sqrt{3}}{4} (10)^2 = \frac{\sqrt{3}}{4} \cdot 100 = 25\sqrt{3} \text{ cm}^2 \]
Since there are two triangular bases, the total area of the triangles is:
\[ 2A = 2 \cdot 25\sqrt{3} = 50\sqrt{3} \text{ cm}^2 \]
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Finding the area of the rectangular faces: The triangular prism has three rectangular faces.
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The first rectangle corresponding to the triangular face has dimensions equal to the height of the triangle and the width of the prism:
- Height = 8 cm (height of the triangle),
- Width = 6 cm (width of the prism).
Area = \( 8 \times 6 = 48 \text{ cm}^2 \).
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The second rectangle corresponds to one side of the triangle:
- Length = 10 cm (side of the triangle),
- Width = 6 cm.
Area = \( 10 \times 6 = 60 \text{ cm}^2 \).
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The third rectangle corresponds to the other side of the triangle:
- Length = 10 cm (other side of the triangle),
- Width = 6 cm.
Area = \( 10 \times 6 = 60 \text{ cm}^2 \).
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Calculating the total area of the three rectangular faces: Total rectangular area:
\[ 48 + 60 + 60 = 168 \text{ cm}^2 \]
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Calculating the total surface area of the prism: Add the area of the two triangular bases and the three rectangular sides:
\[ \text{Total Surface Area} = 50\sqrt{3} + 168 \]
Since \( \sqrt{3} \) is approximately 1.732, we can estimate:
\[ 50\sqrt{3} \approx 50 \times 1.732 \approx 86.6 \]
Thus:
\[ \text{Total Surface Area} \approx 86.6 + 168 \approx 254.6 \text{ cm}^2 \]
Since none of the responses exactly match this, check for common approximations/rounding.
The closest option given would be 260 square centimeters.
Thus, the answer is:
260 square centimeters.