# Square Pyramid

*Go to Surface Area or Volume.*

Square Pyramid Facts

**Notice these interesting things:**

- It has 5 Faces
- The 4 Side Faces are Triangles
- The Base is a Square
- It has 5 Vertices (corner points)
- It has 8 Edges

## Surface Area

When side faces are the same:

**Surface Area** = [Base Area] + \frac{1}{2} × Perimeter × [Slant Length]

### Example: Side faces are the same, slant length is 3, base is square with side length of 5

Surface Area | = [Base Area] + \frac{1}{2} × Perimeter × [Slant Length] | |

= [5 × 5] + \frac{1}{2} × (5+5+5+5) × 3 | ||

= 25 + \frac{1}{2} × 20 × 3 | ||

= 25 + 30 | ||

= 55 |

When side faces are different we can calculate the area of the base and each triangular face separately and then add them up.

## Volume

**Volume** = \frac{1}{3} × [Base Area] × Height

### Example: base is square with side length of 5 , height is 6

Volume | = \frac{1}{3} × [Base Area] × Height | |

= \frac{1}{3} × [5 × 5] × 6 | ||

= \frac{1}{3} × 150 | ||

= 50 |