# 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] + ½ × Perimeter × [Slant Length]

= [5 × 5] + ½ × (5+5+5+5) × 3

= 25 + ½ × 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

Play with it here. Note how the formula stays the same when it "leans over" (*oblique*):

## Other Images

1864, 1865, 1866, 1867