Spinning Square Pyramid - Math Is Fun

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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

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

Pyramid Perimeter and Height

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.

square pyramid

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

Louvre Pyramid 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 Great Pyramids of Egypt 1864, 1865, 1866, 1867 Pyramid vs Cone Pyramids Solid Geometry

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