Square Pyramid
Go to Surface Area or Volume.
A 3D shape with a square base and triangular sides that meet at a single point.
images/polyhedra.js?mode=square-pyramid
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] + 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 = 1 3 × [Base Area] × Height
Think of filling a pyramid-shaped container with water. The volume tells us how much water we need.
Example: base is square with side length of 5 , height is 6
Volume= 1 3 × [Base Area] × Height
= 1 3 × [5 × 5] × 6
= 1 3 × 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
The Louvre Museum in Paris features a modern glass pyramid at its entrance, making a beautiful contrast to the classic museum buildings.
Great Pyramids of Egypt
1864, 1865, 1866, 1867