Ant on a large die

Geometry Level 5

An ant begins at a point P on one edge of an ordinary, but large, cubical die. He visits all 6 faces of the die in the following order: 5, 3, 1, 4, 2, 6, at which point he has returned to P. He takes the shortest possible route for this particular journey, walking 5cm, 10cm, 15cm, 5cm, 10cm, and 15cm respectively on each face.

Find the surface area of the die in cm\(^2\).

Note: The opposite faces on an ordinary die add up to 7.

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