To calculate the total surface area of a triangular prism, we need to find the area of each face and add them up.
The triangular faces have base 5cm and height 12cm, so each one has an area of:
(1/2) x 5cm x 12cm = 30cm²
There are two of these faces, so their combined area is:
2 x 30cm² = 60cm²
The rectangular faces have dimensions 5cm x 10cm and 5cm x 13cm, so their areas are:
5cm x 10cm = 50cm²
5cm x 13cm = 65cm²
Again, there are two of these faces, so their combined area is:
2 x (50cm² + 65cm²) = 230cm²
Finally, we add up the areas of all the faces to get the total surface area:
60cm² + 230cm² = 290cm²
Therefore, the total surface area of this triangular prism is 290cm².