Which of the following figures satisfy the given conditions ?
Figure (i) Faces : 4, Edges : 6, Vertices : 4
Figure (ii) Faces : 5, Edges : 9, Vertices : 6

Options

A.
B.
C.
D.

Answer

To solve the question, we need to analyze the two figures based on the given conditions regarding their faces, edges, and vertices.

### Step-by-Step Solution:

1. **Understanding the First Figure:**
- We need to check if there exists a 3D shape with **4 faces, 6 edges, and 4 vertices**.
- A common shape that fits this description is a **triangular pyramid** (also known as a tetrahedron).
- A triangular pyramid has:
- **Faces**: 4 (1 triangular base + 3 triangular sides)
- **Edges**: 6 (3 edges of the base + 3 edges connecting the apex to each vertex of the base)
- **Vertices**: 4 (1 apex + 3 vertices of the base)

Therefore, the first figure satisfies the conditions.

2. **Understanding the Second Figure:**
- Now, we need to check if there exists a 3D shape with **5 faces, 9 edges, and 6 vertices**.
- A shape that fits this description is a **triangular prism**.
- A triangular prism has:
- **Faces**: 5 (2 triangular bases + 3 rectangular lateral faces)
- **Edges**: 9 (3 edges of one triangle + 3 edges of the other triangle + 3 edges connecting the two triangles)
- **Vertices**: 6 (3 vertices from one triangle + 3 vertices from the other triangle)

Therefore, the second figure also satisfies the conditions.

### Conclusion:
Both figures satisfy the given conditions:
- Figure (i): Triangular Pyramid (4 faces, 6 edges, 4 vertices)
- Figure (ii): Triangular Prism (5 faces, 9 edges, 6 vertices)