# How to find parallelepiped height?

In order to figure out how to find the height of the parallelepiped, we first deal with the concepts.

## Definitions:

A parallelepiped is a polyhedron having six sides, each of which is a parallelogram.

- Parallelepipeds can be inclined or straight.
- An oblique parallelepiped is a parallelepiped in which the faces are not perpendicular to the base.
- A rectangular parallelepiped is a special case where all the faces of a figure are not just parallelograms, but rectangles, and they are perpendicular to the base.
- The height of the parallelepiped is the distance between its two opposite planes (the segment perpendicular to the bases).

Let's consider different ways how to find the parallelepiped height.

## Solutions:

Denote the height by the letter h.

### Method 1. Given the volume and area of the base

#### Formula:

- h = v / s
- Where, V is the volume of the parallelepiped
- S is the area of the base to which the height is drawn.

#### Example:

Volume of inclined parallelepiped ABCDA1B1C1D1equal to 36 cm3, base area ABCD, to which the height is equal to 9 cm2. Find the height.

#### Decision:

- h = 36/9 = 4 (cm)
- Answer: 4 cm.

### Method 2: given the volume and length of the faces

#### Example:

Volume of parallelepiped ABCDA1B1C1D1equal to 36 cm3, The length of the base ABCD to which the height is held is 4 cm, the width is 3 cm. Find the height.

#### Decision:

The formula for height remains the same:

- h = v / s

S is the area of the base and we can find it using the formula:

- S = a * b,

where a and b are sides of a parallelogram, in our case AB and BC. Based on this, we can change the form of the formula by substituting the expression a * b instead of S

We get the formula: h = V / (a * b)

Substitute the numbers:

- h = 36 / (3 * 4) = 36/12 = 3 (cm)
- Answer: 3 cm

### Method 3: Rectangular Box

As we already figured out above, such a parallelepiped is a special case. How to find the height of a rectangular parallelepiped? Very simple - the height is always the same.from one of the faces. Therefore, to find it, no special formulas are required. Here we need formulas to find the length of the faces. For example, the parallelepiped volume formula:

- V = a * b * c, where a, b and c are the faces of the figure.

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