Final answer:
The surface area of the triangular prism is 234 cm², and the volume is 27 cm³.
Step-by-step explanation:
To calculate the surface area of a triangular prism, you need to find the area of the two triangular bases and the three rectangular faces.
The formula for the area of a triangle is 1/2 * base * height.
In this case, the base is 6 cm and the height is 3 cm, so the area of each triangle is 1/2 * 6 cm * 3 cm = 9 cm².
The area of two triangles is 2 * 9 cm² = 18 cm².
The formula for the area of a rectangle is length * width.
The three rectangles have lengths of 12 cm and widths of 6 cm, so the total area of the rectangles is:
3 * (12 cm * 6 cm) = 216 cm².
Adding the area of the triangles and the rectangles gives a total surface area of 18 cm² + 216 cm² = 234 cm².
To calculate the volume of a prism, you need to multiply the area of the base by the height.
The base of the prism is a triangle with a base of 6 cm and a height of 3 cm, so the area of the base is:
1/2 * 6 cm * 3 cm = 9 cm².
Multiplying the area of the base by the height of the prism gives a volume of:
9 cm² * 3 cm = 27 cm³.