Parallelepiped Side Calculator: Find the Length of a Parallelepiped's Sides

In geometry, a side can be defined as a line connecting two vertices of a figure or two-dimensional figure. Our online calculator will help you find the side, edge of more than 11 shapes.

A parallelepiped is a prism based on a parallelogram, or (equivalently) a polyhedron, which has six faces and each of them is a parallelogram.

If you need to find the length of a side of a parallelepiped, our free online parallelepiped side calculator can help. A parallelepiped is a three-dimensional shape with six faces, each of which is a parallelogram. Our calculator can find the length of any side of a parallelepiped given the length of two other sides and the angle between them.

Parallelepiped Side Formulas

There are several formulas that you can use to calculate the length of a side of a parallelepiped. The most common ones involve trigonometry and the Pythagorean theorem.

Parallelepiped Trigonometry Formulas

The following formulas can be used to calculate the length of a side of a parallelepiped using trigonometry:

Formula 1:c = b \dfrac{sin(A)}{sin(B)} where c is the length of the side to be found, b is the length of a known side, A is the angle between the known side and the side to be found, and B is the angle between the known side and a third side.

Formula 2:c = b cos(C) where c is the length of the side to be found, b is the length of a known side, and C is the angle between the two sides.

Parallelepiped Pythagorean Theorem Formula

As in the case of the cube, inside the rectangular parallelepiped, you can draw a diagonal that connects the opposite vertices of the bases. In a right triangle, the diagonal of the parallelepiped d will be the hypotenuse, and the diagonal of the base and the edge will be legs. Then the lateral edge of the parallelepiped can be found through the Pythagorean theorem.

Formula 3:c = \sqrt{d^2 - b^2} where c is the length of the side to be found, b is the length of a known side, and c is the length of the diagonal of the parallelepiped.

Formula 4:a = \sqrt{D^2 - d^2} = \sqrt{D^2 - (b^2 + c^2)} where a is the length of the side(edge) to be found, b and c are the length of the known sides, d is the base diagonal, and D is the length of the diagonal of the parallelepiped.

Example Problems

Here are some examples of how to use the formulas to find the length of a side of a parallelepiped.

Example 1

Find the length of side b in a parallelepiped where a = 4, c = 6, A = 45 degrees, and B = 60 degrees.

We can use Formula 1 to solve for b:

b = a \dfrac{sin(B)}{sin(A)} = 4 \dfrac{sin(60)}{sin(45)} = 5.657

Therefore, the length of side b is approximately 5.657 units.

Example 2

Find the length of side `a` in a parallelepiped where `b` = 10, `b` = 13, and the diagonal length of the parallelepiped is 20.

We can use Formula 4 to solve for c:

a = \sqrt{D^2 - b^2 - c^2} = \sqrt{20^2 - 10^2 - 13^2} = 11.44

Therefore, the length of side a is 11.44 units.