If you have a regular dodecahedron and you slice it in half along a plane that passes through the centres of opposite faces, what is the shape of the cross-section?
- AHexagon
- BDecagon
- CRectangle
- DPentagon
Solution & Step-by-step Explanation
A regular dodecahedron is a 3D solid boundary comprising 12 regular pentagonal faces.
When it is sliced in half by a plane passing through the centres of two directly opposite faces, the cutting plane intersects exactly 10 faces surrounding the axis of symmetry.
Each intersected face contributes one straight edge line segment to the perimeter boundary of the sliced inner plane section. Because it systematically passes through 10 boundary lines, the resulting flat cross-sectional face forms a Decagon (a 10-sided polygon).
When it is sliced in half by a plane passing through the centres of two directly opposite faces, the cutting plane intersects exactly 10 faces surrounding the axis of symmetry.
Each intersected face contributes one straight edge line segment to the perimeter boundary of the sliced inner plane section. Because it systematically passes through 10 boundary lines, the resulting flat cross-sectional face forms a Decagon (a 10-sided polygon).