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------------------------------------------------ Find the surface area of this triangular prism.

A triangular prism has:
- A base of 8 inches,
- A width of 2 inches,
- A height of 6 inches,
- A slant height of 10 inches.

Choose the correct surface area:

A. 128 square inches
B. 176 square inches
C. 192 square inches
D. 224 square inches

To find the surface area of the triangular prism, calculate the area of the two triangular bases and the three rectangular faces. The total surface area is the sum of these areas, which is 192 square inches.

Explanation:

To find the surface area of the triangular prism, we need to calculate the area of the two triangular bases and the three rectangular faces.

Both the bases have the same area, which can be found by using the formula for the area of a triangle: Area = 1/2 x base x height. In this case, the base of the triangle is 8 inches and the height is 6 inches. Therefore, the area of both bases is 1/2 × 8 × 6 = 24 square inches.

Each rectangular face has a length equal to the length of the triangle's base (8 inches) and a height equal to the prism's height (6 inches). So, the area of each rectangular face is 8 × 6 = 48 square inches.

The total surface area of the triangular prism is the sum of the areas of the two triangular bases and the three rectangular faces: 24 + 24 + 48 + 48 + 48 = 192 square inches. Therefore, the correct answer is c. 192 square inches.