Pyramidal Frustum

Let $s$ be the slant height, $p_i$ the top and bottom base Perimeters, and $A_i$ the top and bottom Areas. Then the Surface Area and Volume of the pyramidal frustum are given by

$$S = {\textstyle{1\over 2}}(p_1+p_2)s$$

$$V = {\textstyle{1\over 3}} h(A_1+A_2+\sqrt{A_1A_2}\,).$$

See also Conical Frustum, Frustum, Pyramid, Spherical Segment, Truncated Square Pyramid

References

Beyer, W. H. (Ed.) CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 128, 1987.

Dunham, W. Journey Through Genius: The Great Theorems of Mathematics. New York: Wiley, pp. 3-4, 1990.