Find the sum of number of faces, edges and vertices of a tetrahedron.

Options

A. 16
B. 14
C. 24
D. 20

Answer

To find the sum of the number of faces, edges, and vertices of a tetrahedron, we can follow these steps:

### Step 1: Identify the number of faces in a tetrahedron.
A tetrahedron is a type of pyramid with a triangular base. It has:
- 4 triangular faces (1 base triangle + 3 triangular sides).

**Hint:** Remember that each triangular side connects to the base triangle.

### Step 2: Identify the number of edges in a tetrahedron.
Next, we count the edges. A tetrahedron has:
- 6 edges (3 edges from the base triangle + 3 edges connecting the apex to each vertex of the base).

**Hint:** Count the edges of the base triangle first, then add the edges connecting the apex.

### Step 3: Identify the number of vertices in a tetrahedron.
Now, we count the vertices. A tetrahedron has:
- 4 vertices (3 vertices from the base triangle + 1 apex vertex).

**Hint:** Consider the corners of the base triangle and the top point.

### Step 4: Calculate the sum of faces, edges, and vertices.
Now, we add the numbers we found:
- Number of faces = 4
- Number of edges = 6
- Number of vertices = 4

So, the sum is:
\[ 4 \text{ (faces)} + 6 \text{ (edges)} + 4 \text{ (vertices)} = 14 \]

### Final Answer:
The sum of the number of faces, edges, and vertices of a tetrahedron is **14**.

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