A light and a shadow

Geometry Level 2

A rectangular billboard \(ABCD \) is illuminated by a lantern \(E \) and casts a shadow in the \(xy \)-plane. The positions \((x,y,z)\) of the lantern and the billboard's vertices are \[A = (0,0,0), \quad B = (0,3,0), \quad C = (0,3,2), \quad D = (0, 0 ,2), \quad E = (3, -1, 4). \] What is the area of the shadow?

Assumptions: The light source is a point and the billboard has zero thickness. The ground is the \(xy\)-plane.

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