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Cube in a characteristic position

Place a cube of edge 4.5 u resting on the PH on a face and work out its height.

Step-by-step solution

1. The height changes with the position: face, edge or vertex.
2. Resting on a face, the height is the edge a.
3. Resting on an edge, the height is the diagonal of a face: a√2.
4. Resting on a vertex, the height is the diagonal of the cube: a√3.

Result: height = 4.5 u (4.5 u).

Before drawing the elevation, work out the height: it is the length to carry from the base.

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