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

## Side

## Parallelepiped

## Parallelepiped side calculator

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.

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