To find the surface area of a triangular prism, you need the area of the triangular base and the area of the three rectangular sides.
Given your numbers: 10, 10, 8, 10, 6.
Let's assume the triangular base has sides of lengths 10 cm, 10 cm (two equal sides, indicating it's isosceles), and 8 cm (the base). The height corresponding to the base of 8 cm would need to be calculated or given, but since you provided sides, let's calculate with an approximate height.
For an isosceles triangle, you can find the height (h) using the formula:
\[ h = \sqrt{a^2 - \left(\frac{b}{2}\right)^2} \] where \( a \) is the length of the equal sides (10 cm) and \( b \) is the base of the triangle (8 cm):
\[ h = \sqrt{10^2 - \left(\frac{8}{2}\right)^2} = \sqrt{100 - 16} = \sqrt{84} \approx 9.17 , \text{cm}. \]
The area of the triangular base \( A \) is given by \[ A = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 8 \times 9.17 \approx 36.68 , \text{cm}^2. \]
The three rectangular sides (let's assume the height of the prism is one of the provided numbers, say 10 cm):
- Rectangle with dimensions 8 cm (base triangle side) x 10 cm (height of prism) = 80 cm²
- Rectangles with dimensions 10 cm (equal side) x 10 cm = 100 cm² each (there are two of these)
So, the total surface area \( SA \) is given by:
\[ SA = 2 \times \text{Area of triangle} + \text{Area of rectangles} \] \[ SA = 2 \times 36.68 + 80 + 2 \times 100 = 73.36 + 80 + 200 = 353.36 , \text{cm}^2. \]
However, none of the responses match that, and since I can’t confirm the proper parameters without a clear height of the prism, I would advise selecting from the options given.
Based on typical triangular prism surface area values among your options, 180 square centimeters is a likely candidate as it seems reasonable with conventional dimensions.
Final Answer: 180 square centimeters.