Look at the cut inside the solid
A cross-section is the flat shape where a cutting plane passes through a solid. Count the straight edges inside the solid, not its outer silhouette or the rectangular border of the plane sheet. This level cut crosses four upright faces of the block, making a rectangle. Other cuts can make three, four, five or six sides.
Follow a cut near a corner
This plane cuts off a corner of the cube and crosses three faces. Each crossed face contributes one straight edge. Follow those three edges around the cut: they form a triangle. The second drawing shows the same section viewed straight on, without the cube around it.
Try a different tilted cut
The new plane cuts farther into the cube at a different tilt. The lines on the front faces show where the plane meets the cube. Continue the cut across the hidden faces, then count all the sides of the section.
Try it
How many sides does this new cross-section have?
- Four sides: a rectangle.
- Five sides: a pentagon.
Show the answer
Five sides: a pentagon.
Five cube faces each contribute one edge, so the section is a pentagon. The plane sheet’s rectangular border extends outside the cube and does not set the section’s shape. Include the edges on the hidden faces.
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