You're that close to the correct answer . . .
The surface area of the original cube is: .6 × 7² = 294 m².
When that corner is sliced off, we lose three isosceles right triangles
. . Each has 4m legs and an area of 8 m².
Then we gain an equilateral triangle with side 4√2 m.
. . Its area is: 8√3 m².
The final surface area is: .294 - 3(8) + 8√3 .≈ .283.86