# Parallelogram Calculator

## Parallelogram definition

A parallelogram is a quadrilateral, or a four-sided polygon, where both pairs of opposite sides are parallel and equal in length. It can be represented as a flat shape with four sides, two pairs of parallel lines, and four angles.

## Parts of a Parallelogram

The seven parts of a parallelogram mentioned in this tool are base length, side length, height, area, perimeter, smaller angle and larger angle.

### Base length (a)

The term base refers to the length of one side and "height" to the length of a perpendicular segment between that side and the opposite parallel side. Any side of a parallelogram can be a base.

It can be found with the following formulas:

• If you know the area and height of the parallelogram:

`a = A / ha`

• If you know the perimeter and the side length:

`a = (P - 2 * b) / 2`

• If you know the area, side length and one of the angles:

`a = A / b / sin(β)`, or `a = A / b / sin(α)`

### Side length (b)

The side length of a parallelogram is the length of its adjacent side to the base. It is usually denoted by b.

You can determine it with these formulas:

• If you know the perimeter and base length:

`b = (P - 2 * a) / 2`

• If you know the height and one of the angles:

`b = ha / sin(α)`, or `b = ha / sin(β)`

• If you know the area, base length and one of the angles:

`b = A / a / sin(β)`, or `b = A / a / sin(α)`

### Height (ha)

The height of a parallelogram is the distance between its two parallel sides. It is perpendicular to the base and is usually denoted by h.

• If you know the base length and area:

`ha = A / a`

• If you know the side length and one of the angles:

`ha = b * sin(β)`, or `ha = b * sin(α)`

### Area (A)

The area of a parallelogram can be calculated by multiplying its base length and height. The formula to calculate the area of a parallelogram is given by:

`A = a * ha`

### Perimeter (P)

The perimeter of a parallelogram is the total length of its four sides. The formula to calculate the perimeter of a parallelogram is given by:

`P = 2 * (a + b)`

### Smaller angle (α)

In a parallelogram, there exist two pairs of angles. Among these, the lesser angles refer to the smaller ones. Since the total sum of angles within a parallelogram equals 360°, and there are two pairs of congruent angles, it follows that the sum of the lesser angle and its counterpart is 180°.

Thus, the calculation for the smaller angle is as follows:

`α = 180 - β`

However, if you do not know the size of the larger angle, you can calculate the smaller angle using the heigth and side length of the parallelogram:

`α = asin(ha / b)`

### Larger angle (β)

Similarly to the smaller angle mentioned above, the larger angle can be determined by subtracting the smaller angle from 180°.

`β = 180 - α`