Applying Pythagoras’ Theory to 3D representations

Task goals

• Find the diagonal across a face of a cuboid using Pythagoras' theorem.
• Find the space diagonal of a cuboid using a two-step method: first find a face diagonal, then apply Pythagoras again.
• Identify which face diagonal to use and recognize when multiple applications of the theorem are needed in 3D problems.
• Apply Pythagoras' theorem to 3D contexts such as rods fitting inside boxes, cables across rooms, and supports on 3D structures.
• Justify whether a given length can or cannot fit inside a 3D shape by calculating its space diagonal.