To find the total surface area, you need to find the area of the three rectangles and two triangles of that prism.
Area of the two triangles
= 2 x 1/2 x 12 x 5
= 60
Area of the bottom rectangle
= 12 x 24
= 288
Area of the standing rectangle
= 5 x 24
= 120
To find the area of the sloping rectangle, you need to find the length of one side of it. You do that by finding the hypotenuse of the triangle.
So, hypotenuse of the triangle
= square root of (5 squared + 12 squared)
= 13
Area of sloping rectangle
= 24 x 13
= 312
Total surface area of prism
= 60 + 288 + 120 + 312
= 780.
Hopefully that helped. :)