Shadowy areas

[bonanova]

If I hold an illuminated sphere in front of a screen, it casts a circular shadow whose area is exactly 1/4 of the area of the sphere. Now let the object have protrusions, but remain convex -- as for example a tetrahedron. Will its "bumpiness" create a shadow area that is greater than 1/4 of its surface area, on average?

[Brainy Binary]

Spoiler

The triangle shadow  is 1/4 its area at far away light source perpendicular to a base, but a bigger shadow can be created by rotating the tetrahedron making rectangle shadow.

 

[bonanova]

On 1/12/2016 at 10:41 AM, Brainy Binary said:

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The triangle shadow  is 1/4 its area at far away light source perpendicular to a base, but a bigger shadow can be created by rotating the tetrahedron making rectangle shadow.

 

@Brainy Binary, What you say is true. But note the OP asks about the average or expected shadow area.