Spinning Triangular Pyramid - Math Is Fun

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Triangular Pyramid

triangular pyramid

Jump to Surface Area or Volume

Imagine a pyramid made entirely of triangles, including its base (instead of the more familiar square base).

It's one of the simplest and most elegant 3D shapes.

Triangular Pyramid Facts

Notice these interesting things:

  • It has 4 faces
  • The 3 side faces are triangles
  • The base is also a triangle
  • It has 4 vertices (corner points)
  • It has 6 edges
  • It is also a tetrahedron
images/polyhedra.js?mode=tetrahedron

Surface Area

triangular pyramid height, side length and perimeter

The surface area is the total area of all its faces. When the three side faces are the same we can use this shortcut formula:

Surface Area = [Base Area] + 1 2 × Perimeter × [Slant Length]

Example: Base Area is 28, Perimeter is 20, Slant length is 5

Surface Area = [Base Area] + 1 2 × Perimeter × [Slant Length]= 28 + 1 2 × 20 × 5= 28 + 50= 78

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

This works because a pyramid's volume is-one-third that of a prism with the same base and height.

Example: base area is 28, height is 4.5

Volume= 1 3 × [Base Area] × Height= 1 3 × 28 × 4.5= 1 3 × 126= 42 Tetrahedron Pyramids Square Pyramid Why is a Pyramid like a Cone? Solid Geometry

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