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.

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.