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Square Pyramid Volume (Base and Height)

Find the volume of a right square pyramid from its base edge and height, plus base area, slant height, lateral area and surface area.

Input

Enter the base edge and the height of a right square pyramid to calculate its volume. The base area, slant height, lateral area and surface area are also shown.

Result

a = 6h = 8

Volume

96

Base area

36

Slant height

8.544004

Lateral area

102.528045

Surface area

138.528045

Lengths use the same unit as the input. Areas are squared and the volume is cubed.

How it works

  • The volume equals one third of the base area times the height. Since the base area is the edge a squared, the volume is one third times a squared times h.
  • The slant height is the height of each triangular face. It is found from the pyramid height h and half of the base edge using the Pythagorean theorem.
  • The four triangular faces are congruent, so the lateral area is the base edge times the slant height for one face, giving two times a times the slant height in total.
  • The surface area is the base area plus the lateral area. Use consistent length units, and areas come out squared and the volume cubed.

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