We need to first calculate the area of each face of the prism and then add them together to find the total surface area.
The top and bottom faces of the prism are rectangles with dimensions 12 cm by 17 cm, so each face has an area of:
12 cm x 17 cm = 204 cm²
The front and back faces of the prism are trapezoids with bases 8 cm and 13 cm, height 4 cm, and slant height √(4² + (13-8)²) = √(16 + 25) = √41 cm. Therefore, each face has an area of:
1/2 x (8 cm + 13 cm) x 4 cm x √41 cm ≈ 100.07 cm²
The left and right faces of the prism are trapezoids with bases 8 cm and 13 cm, height 17 cm, and slant height √(17² + (13-8)²) = √(289 + 25) = √314 cm. Therefore, each face has an area of:
1/2 x (8 cm + 13 cm) x 17 cm x √314 cm ≈ 571.69 cm²
To find the total surface area, we add up the areas of all six faces:
Total surface area = 2(204 cm²) + 2(100.07 cm²) + 2(571.69 cm²) = 1743.52 cm²
Therefore, the surface area of the prism is 1743.52 cm².