Rectangular Frustum Calculator

Name: Rectangular Frustum - Geometry Calculator
Author: Jürgen Kummer

Calculations for a rectangular frustum. This is a rectangular pyramid with a truncated apex, or a general frustum with a rectangle as the base. At the cut surface is another rectangle, similar to the one at the base, but smaller. So both rectangles have the same length-to-width ratio.
Enter three of the four side lengths a, b, c and d, as well as the height h. Choose the number of decimal places, then click Calculate.

Formulas:

\frac{a}{c} = \frac{b}{d}

e = \sqrt{h^{2} + {[\frac{a - c}{2}]}^{2} + {[\frac{b - d}{2}]}^{2}}

s_{1} = \sqrt{h^{2} + {[\frac{a - c}{2}]}^{2}}

s_{2} = \sqrt{h^{2} + {[\frac{b - d}{2}]}^{2}}

A = a b + c d + (a + c) \cdot s_{2} + (b + d) \cdot s_{1}

V = \frac{h}{3} \cdot (a b + c d + \sqrt{a b c d})

Lengths, widths and heights have the same unit (e.g. meter), the area has this unit squared (e.g. square meter), the volume has this unit to the power of three (e.g. cubic meter). A/V has this unit ^-1.

The faces of the rectangular frustum are four isosceles trapezoids. Two of them, opposite each other, have side lengths a and c and leg lengths e. The other two, also opposite each other, have side lengths b and d and leg lengths e.
The two rectangles ab and cd are parallel, centered, and aligned one above the other. The slant edges e are the edges between the corresponding vertices of the two rectangles. The two slant heights are the distances between the corresponding parallel sides of the two rectangles. s₁ is the distance between the lengths, and s₂ is the distance between the widths. e is greater than each s₁ and s₂. If the lengths are greater than the widths, then s₁ is greater than s₂.

Such shapes are frequently found in architecture, for example as plinths or sockets. They are also used for packaging, kitchenware, and similar purposes.

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