Square Pyramid Volume (from Base and Edge)

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

Input

Enter the base edge and the lateral edge of a right square pyramid to get its height, slant height, volume, and surface area.

Base edge a

Lateral edge l

Volume V

81.38796

Height h

6.78233

Slant height m

7.416198

Surface area S

124.994382

Length units match the input, while area is squared and volume is cubed.

This tool assumes a right square pyramid whose square base has its center directly below the apex.
With base edge a and lateral edge l, the height is h equal to the square root of l squared minus a squared over 2.
Volume is V equal to one third times a squared times h.
The slant height from the midpoint of a base edge to the apex is m equal to the square root of l squared minus a squared over 4.
Surface area is the base a squared plus four triangular faces 2am, giving S equal to a squared plus 2am.
Length units match the input, area units are squared, and volume units are cubed.
If the lateral edge is too short for a valid solid, when l squared is at most a squared over 2, the volume cannot be computed.

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