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Square Pyramid 3-D Formula

In geometry, a square pyramid is a pyramid having a square base. If the apex is perpendicularly above the center of the square, it will have C4v symmetry. The Square Pyramid Formula is as follows:

Area of Base (A) = s²
Surface Area of Pyramid = s² + 2sl = A + 2sl
Volume of Pyramid = (1/3)b²h

where
        s,b = side, h = height and l = slant height

If the sides are all equilateral triangles, the pyramid is one of the Johnson solids referred to as J1. The 92 Johnson solids were named and described by Norman Johnson in 1966. The Johnson square pyramid is characterized by a single edge-length parameter a. The height H from the midpoint of the square to the apex, the surface area A including all five faces and the volume V of such a pyramid is:

H=\frac{1}{\sqrt{2}}a

A=(1+\sqrt{3})a^2

V=\frac{\sqrt{2}}{6}a^3

Other square pyramids have isosceles triangle sides. For square pyramids in general, with base length l and height h, the surface area and volume are:

A=l^2+l\sqrt{l^2+(2h)^2}

V=\frac{1}{3}l^2h.

 
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