PK 2019 Q17
17. The diagram shows a net of an octahedron. When this is folded to form the octahedron, which of the labelled line segments will coincide with the line segment labelled \(x\)?
- A
- B
- C
- D
- E
Pink Kangaroo 2019, Question 17. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E
The four triangles on the left will fold to form one square-based pyramid (without the base). The four triangles on the right will fold to make another pyramid, with the two pyramids hinged at the dashed edge. When these two pyramids are folded at this edge, the bottom end of \(x\) will coincide with the right-hand end of E; so \(x\) will coincide with E.
Solution © UK Mathematics Trust, from the PK 2019 solutions.