Find the surface area of a triangular prism if the area of its cross section is 34cm2, its length is 45cm and the three sides of the triangular ends add up to 27cm.

To find the surface area of a triangular prism, you need to add the area of the two triangular ends and the area of the three rectangular sides.

1. The area of the two triangular ends is simply twice the area of one of them. Since the area of the cross section (which is a triangle) is given as 34 cm², the total area of the two ends is 2 * 34 cm² = 68 cm².

2. The three sides of the triangular ends add up to 27 cm. This is the perimeter of the triangle. Each of these sides forms one side of a rectangle, with the length of the prism as the other side. So, the total area of the three rectangular sides is the perimeter of the triangle times the length of the prism, which is 27 cm * 45 cm = 1215 cm².

3. Finally, add the area of the two ends and the area of the sides to get the total surface area of the prism. So, the total surface area is 68 cm² + 1215 cm² = 1283 cm².