Calculations at a polyhedron shaped like an ingot. This is made of two regularly opposite, parallel rectangles. These have the same ratio of length and width and are connected at their corners.
Enter three of the four lengths and widths of the rectangles, as well as the ingot height. Choose the number of decimal places, then click Calculate.
Formulas:
a / b = a' / b'
s = √ h² + ( a - a')² / 4 + ( b - b')² / 4
i = √ h² + ( a - a' )² / 4
j = √ h² + ( b - b' )² / 4
d = √ h² + ( a + a')² / 4 + ( b + b')² / 4
A = ab + a'b' + i(a+a') + j(b+b')
V = h/3 * ( ab + √ ab*a'b' + a'b' )
Lengths, widths, heights and diagonal 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.
This shape of an ingot is also known as a rectangular frustum. The latter is arguably the more fitting name for a geometric object, but the name ingot establishes a connection to a real-world object. The ingot does not have any naming reference to the rectangular pyramid from which it could be derived.
It is probably quite common for geometric solids to have multiple appropriate names. Of course, such names depend on the context in which they are used. When referring to ingots or similar objects, rectangular frustum isn't a name that immediately springs to mind. Therefore, nearly identical calculators for the same shapes may appear multiple times here, possibly not just this one, as these pages have been developed over several decades. Depending on the context in which the individual calculators were created, these identical shapes are treated differently. The mathematical foundations are, of course, the same, but formulas may be structured differently, use different terminology, and sometimes even calculate different values. For example, this calculator for the ingot also determines the length of the space diagonal, while the calculator for the rectangular truncated pyramid does not.