# Oblique Prism

An oblique prism is a slanted prism in which the lateral faces are not perpendicular to the bases. As a result, the 2 bases are not aligned perfectly above one another when the prism rests on its base. The lateral face of an oblique prism is not its height.

The height of an oblique prism is calculated from outside the shape. The figure below shows an oblique prism and how it differs from a right prism.

## Formulas

### Surface Area

The surface area of an oblique prism can be calculated as 2 × base area + areas of the parallelograms. In an oblique prism, the lateral faces are parallelogram-shaped and may or may not be congruent every time based on the different shapes of the prisms.

Since there is no direct formula to calculate the surface area of an oblique prism, it is not in common practice.

### Volume

The volume of an oblique prism is its space occupied in the three-dimensional plane. It is the same as the volume of a right prism having the same height. We measure the volume in cubic units such as m3, cm3, mm3, ft3.

The formula to calculate the volume of an oblique prism is given below:

Volume (V) = Base Area × Height

## Solved Examples

Find the volume of an oblique rectangular prism given in the figure.

Solution:

Here, Base Area = Length × Width
= 8 × 7
= 56 cm2
As we know,
Volume (V) = Base Area × Height, here base area = 56 cm2, height = 16 cm,
V = 56 × 16
= 896 cm3

Find the volume of an oblique triangular prism whose base area is 11 cm2 and height is 9 cm.

Solution:

As we know,
Volume (V) = Base Area × Height, here height = 9 cm, base area = 11 cm2
V = 11 × 9
= 99 cm3

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