Explanation:

Let the dimensions of the rectangular parallelepiped be x, y and z
Then x + y + z = 24
Length of the diagonal
√(x²+y²+z²) = 15
x² +y² + z² = 225
Now , (x+y+z)² = x²+y²+z²+2(xy+yz+zx)
(24)² = 225+2(xy+yz+zx)
2(xy+yz+zx) = 576-225 =351
Total surface area = 2(xy+yz+zx) = 351 cm²