Calculations at an oblique prism. Different to a right prism, the sides are not perpendicular to the bases (angle of slope ≠ 90°). Cavalieri's principle says, that the volume of the oblique prism is similar to that of the right prism with equal base and height. The surface area can be calculated as twice the base area plus the areas of the lateral parallelograms. Enter angle and side length or height and base area or volume. Choose the number of decimal places, then click Calculate. Please enter angles in degrees, here you can convert angle units.
Formulas:
a = h / sin( α )
V = As * h
These formulas also apply to a generalized, oblique cylinder.
Length and height 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).
An oblique prism is inherently asymmetric, as the symmetries are lost due to the obliquity. However, if the base is point-symmetric, then it is also point-symmetric about its central point.
The formula for calculating the volume of an oblique prism or oblique cylinder comes from the Italian astronomer and mathematician Bonaventura Francesco Cavalieri. He discovered in the 17th century that the obliquity does not affect the volume if the height remains constant. The obliquity is irrelevant because the vertical cross-section of the prism always corresponds to its base area, i.e., it is always the same. This is true even though the sides become longer the more oblique the prism is, since the cross-sections are cut according to the height. This can be illustrated by a stack of paper, whose volume does not change even when tilted. This discovery is considered a step in the development of infinitesimal calculus by Leibniz and Newton some decades later.
