ONE-EIGHTH STAGE 2025
Anlo SHS: 31 points
Mpraeso SHS: 35 points
Mfantsiman Girls' SHS: 27 points
Pope John SHS & Minor Seminary: 58 points
Ghana SHS, Tamale: 25 points
Awudome SHS: 23 points
Swedru Secondary School: 36 points
Kumasi High School: 31 points
Anlo SHS: 30 points
ROUND 5 - RIDDLE
RIDDLE
I am a solid geometrical figure.
I have four faces.
I have six edges.
I have four vertices.
Who am I?
ANSWER: TETRAHEDRON
EXPLANATION:
A tetrahedron has $4$ triangular faces, $6$ edges and $4$ vertices.
Hence, I am a tetrahedron.
---
PRACTICE QUESTIONS
1. RIDDLE:
I am a solid geometrical figure.
All my faces are flat polygons.
I have five faces.
I have fewer than ten edges.
My faces are not all congruent.
I have nine edges and six vertices.
Who am I?
ANSWER: TRIANGULAR PRISM
EXPLANATION:
A triangular prism has 2 triangular ends and 3 rectangular faces: 5 faces, 9 edges, 6 vertices.
The square-based pyramid also has 5 faces, but 8 edges and 5 vertices.
2. RIDDLE:
I am a solid geometrical figure.
All my faces are flat polygons.
I have five faces.
I have fewer than ten edges.
At least two of my faces are triangles.
I have eight edges and five vertices.
Who am I?
ANSWER: SQUARE-BASED PYRAMID
EXPLANATION:
A square-based pyramid has 1 square base and 4 triangular faces: 5 faces, 8 edges, 5 vertices.
Check with Euler: $5 - 8 + 5 = 2$
3. RIDDLE:
I am a solid geometrical figure.
All my faces are flat polygons.
I have seven faces.
At least one of my faces is not a triangle.
I have more than ten edges.
I have fifteen edges and ten vertices.
Who am I?
ANSWER: PENTAGONAL PRISM
EXPLANATION:
A pentagonal prism has 2 pentagonal ends and 5 rectangles: 7 faces, 15 edges, 10 vertices.
The hexagonal pyramid also has 7 faces, but 12 edges and 7 vertices.
4. RIDDLE:
I am a solid geometrical figure.
All my faces are flat polygons.
All my faces are triangles.
All my faces are congruent.
I have more than five vertices.
I have eight faces, twelve edges and six vertices.
Who am I?
ANSWER: OCTAHEDRON
EXPLANATION:
A regular octahedron has 8 equilateral triangles, 12 edges and 6 vertices.
Check with Euler: $6 - 12 + 8 = 2$
5. RIDDLE:
I am a solid geometrical figure.
All my faces are flat polygons.
I have seven faces.
I have more than ten edges.
I have fewer than sixteen edges.
I have twelve edges and seven vertices.
Who am I?
ANSWER: HEXAGONAL PYRAMID
EXPLANATION:
A hexagonal pyramid has 1 hexagon and 6 triangles: 7 faces, 12 edges, 7 vertices.
The pentagonal prism also has 7 faces, but 15 edges and 10 vertices.
6. RIDDLE:
I am a solid geometrical figure.
All my faces are flat polygons.
All my faces are triangles.
All my faces are congruent.
I have fewer than eight vertices.
I have an odd number of vertices.
I have six faces, nine edges and five vertices.
Who am I?
ANSWER: TRIANGULAR BIPYRAMID
EXPLANATION:
Two tetrahedra joined face to face give 6 triangular faces, 9 edges and 5 vertices.
The pentagonal bipyramid also has triangular faces and an odd number of vertices, but it has 10 faces, 15 edges and 7 vertices.