The diagram shows how the surface area can be "flattened" into two rectangles, one for the end triangles that is 6 cm by 5.3 cm, and one for the lateral area that is 13 cm by 19.3 cm.
The total area is
.. (6 cm)*(5.3 cm) +(13 cm)*(19.3 cm)
.. = 31.8 cm^2 +250.9 cm^2
.. = 282.7 cm^2