Explanation:

Let the length, breadth and height of the cuboid be l, b and h, respectively.
∴l²+b²=13²=169....(1)
b²+h²=(√281)²=281....(2)
h²+I²=20²=400...(3)
Adding eq (1), (2) and (3), we have
2(l²+b²+h²)=850
⇒l²+b²+h²=425....(4)
From (1) and (4), we have
h²=425−169=256
⇒h=16units
Similarly, l = 12 units andb = 5 units
Therefore, total surface area of thecuboid = 2(lb + bh + hl)
=2(12×5+5×16+16×12)
= 664 square units