Projected Cubes
Geometry
Level
2
If a cube with sides of length X is projected onto a plane, will the area of the projected cube be the same no matter the angle of rotation on the cube?
Not enough information
Yes
No
Depends on Size
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1 solution
If the cube is positioned so that any one side is on the plane (so that the projection looks like a square), the area of that square is X^2. If I rotate the cube 45 degrees on the x and z axis, then the area of the projection is the area of a regular hexagon, or 6 times the area of an equilateral triangle with base X and height ( X 3 ) / 2 , which is not equal to X^2.