Italian mathematical olympiad 2002, problem 2
Source:
February 13, 2012
geometry proposedgeometry
Problem Statement
The plan of a house has the shape of a capital , obtained by suitably placing side-by-side four squares whose sides are metres long. The external walls of the house are metres high. The roof of the house has six faces, starting at the top of the six external walls, and each face forms an angle of with respect to a horizontal plane.
Determine the volume of the house (that is, of the solid delimited by the six external walls, the six faces of the roof, and the base of the house).