Square Pyramid

Go to Surface Area or Volume.

A 3D shape with a square base and triangular sides that meet at a single point.

Square Pyramid Facts

Square pyramid with a blue base and four triangular sides

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
images/polyhedra.js?mode=square-pyramid

Surface Area

Square pyramid diagram labeling the base perimeter and the slant height of a side

When side faces are the same:

Surface Area = [Base Area] + 12 × 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

Square pyramid net

We can also calculate the area of the base and each triangular face separately and then add them up.

Handy if side faces are different.

Volume

Square pyramid with a blue base and four triangular sides

Think of filling a pyramid-shaped container with water. The volume tells us how much water we need.

Volume = 13 × [Base Area] × Height

The height is at right angles to the base.

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

Volume= 13 × [Base Area] × Height= 13 × [5 × 5] × 6= 13 × 150= 50

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

images/geom-oblique-3d.js?mode=pyr4

Other Images

Modern glass square pyramid at the entrance of the Louvre Museum in Paris
The Louvre Museum in Paris features a modern glass pyramid at its entrance, making a beautiful contrast to the classic museum buildings.
The Great Pyramids of Giza in the Egyptian desert
Great Pyramids of Egypt
1864, 1865, 1866, 1867
Pyramid vs Cone Pyramids Solid Geometry