How many faces do a square pyramid has ?

Answer

To determine how many faces a square pyramid has, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Shape**: A square pyramid consists of a square base and triangular faces that connect the base to a single apex (top point).

2. **Identify the Base**: The base of the square pyramid is a square. This contributes **1 face** to the total count.

3. **Count the Triangular Faces**: Each side of the square base has a triangular face that connects to the apex. Since a square has **4 sides**, there are **4 triangular faces**.

4. **Calculate the Total Faces**: Now, we add the faces together:
- 1 (square base) + 4 (triangular faces) = **5 faces** in total.

5. **Verification Using Euler's Formula**: We can confirm our count using Euler's formula, which states:
\[ F + V = E + 2 \]
Where:
- \( F \) = number of faces
- \( V \) = number of vertices
- \( E \) = number of edges

For a square pyramid:
- Faces (F) = 5
- Vertices (V) = 5 (4 at the base + 1 at the apex)
- Edges (E) = 8 (4 edges of the base + 4 edges connecting the apex to each vertex of the base)

Plugging into Euler's formula:
\[ 5 + 5 = 8 + 2 \]
\[ 10 = 10 \]
This confirms that our count of faces is correct.

### Final Answer:
A square pyramid has **5 faces**.

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