A light and a shadow

Geometry Level 2

A rectangular billboard ABCDABCD is illuminated by a lantern EE and casts a shadow in the xyxy -plane. The positions (x,y,z)(x,y,z) of the lantern and the billboard's vertices are A=(0,0,0),B=(0,3,0),C=(0,3,2),D=(0,0,2),E=(3,1,4).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 xyxy-plane.

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