# How to find the height of a parallelogram?

A parallelogram is a quadrilateral with opposing and pairwise parallel sides.

The height of a parallelogram is a line perpendicular to one side of the parallelogram and connecting this side with the opposite angle.

In order to find out how to find the length of the height of a parallelogram, let us turn to the formulas. The height is most often indicated by the letter h.

The method of finding the height depends on the quantities known to us in the task. Let's consider different ways on concrete examples.

## Example 1

The area (S) and the length of the base (a) are given.

- Formula: h = S / a

Example: The area of a parallelogram is 100 cm2, the base to which the height is drawn is 20 cm. Find the height.

- h = 100/20 = 5
- Answer: 5 cm

## Example 2

The length of the side of the parallelogram adjacent to the height (b) and the angle opposite to the height (a) are given.

- The formula: h = b * sin a

Example: Let's designate our parallelogram with the letters ABCD, the height BE passes from the angle ABC to the side AD. The length of the side AB is 20 cm, the angle BAD is 30 degrees. Find the height.

Decision:

- h = 20 * sin 30 ° = 20 * 0.5 = 10

Answer: 10 cm

## Example 3

The length of the side of the parallelogram adjacent to the height (n) and the length of the side cut off from the base (m) are given.

Formula:

- h = root of (n2- m2)

Example: in the parallelogram ABCD, the height BE passes from the angle ABC to the side AD. The length of AB is 5 cm, the length of AE is 3 cm. Find the height.

Decision:

- h = root of (AD2- AB2)
- h = root of (52-32) = 4
- Answer: 4 cm

## Example 4

The length of the diagonal coming from the same angle as the height (d) and the length of the side cut off from the base (m) are given.

Formula:

- h = root of (d2- m2)

Example: in the parallelogram ABCD, the height BE passes from the angle ABC to the side AD. The diagonal of BD is 5 cm, the length of ED = 4 cm.

- h = root of (BD2- ED2)
- h = root of (52- 42) = 3
- Answer: 3 cm

If in the job it is required to find a large height of the parallelogram, then it is necessary to calculate the lengths of both heights and choose the largest value.