# Parallelogram Formula

## Parallelogram Formula

The Greek word “Parallelogrammon,” which means “bounded by parallel lines,” is the source of the English word “Parallelogram.” Thus, a quadrilateral with parallel lines as its borders is referred to as a “parallelogram.” The opposing sides of this shape are parallel and equal. Each of the three primary varieties of parallelograms—square, rectangle, and rhombus—has distinct characteristics. A quadrilateral with two pairs of parallel and equal sides is referred to as a “parallelogram.” If the two pairs of opposite sides in a quadrilateral are equal, then the quadrilateral is said to be a parallelogram.

A quadrilateral is a parallelogram if two of its opposite sides are parallel and equal; likewise, a quadrilateral is a parallelogram if its diagonals cut through one another. In this section, along with the solutions to the problems, students will learn what a parallelogram is, how to find its area, and other information related to them. A parallelogram is a shape with only two dimensions. It has four sides, two pairs of which are parallel while the other two aren’t. A parallelogram has opposite sides that are the same length, opposite angles that are the same size, and its neighbouring angles added together make up 180 degrees.

### What Is Parallelogram Formula?

A unique variety of quadrilaterals made up of parallel lines is called a Parallelogram. A parallelogram can have any angle between its neighbouring sides, but it must have opposite sides that are parallel for it to be a parallelogram. If the opposite sides of a quadrilateral are parallel and congruent, it will be a parallelogram. Consequently, a quadrilateral in which both pairs of opposite sides are parallel and equal is referred to as a “parallelogram.” The parallelogram formula is h = parallelogram height.a = side of the parallelogram (AD) x = any angle between the sides of the parallelogram (∠DAB or ∠ADC).

### Area of a Parallelogram Formula

A two-dimensional plane occupies the space or surface that makes up a parallelogram’s area. Students can examine the Parallelogram Formula.

Parallelogram Formula area Using Base and Height

Parallelogram Formula area: Base* Height

Parallelogram Formula Area Without Height: Area of a Parallelogram  a b sin A = b a sin B

Trigonometry can be used to calculate the area of a parallelogram in the absence of the parallelogram’s height.

Parallelogram Formula area: a b sin A = b a sin B

Diagonal Area of a Parallelogram

Any parallelogram’s area can also be computed using the lengths of its diagonals.

If the diagonals d1 and d2 were to connect at an angle of x, the parallelogram’s area would be given by:

Parallelogram Formula area: 1/2 d1* d1 sin (x)

Area of the parallelogram ABCD is equal to 1/2 AC BD sin (x)

### Perimeter of a Parallelogram Formula

The total distance between a parallelogram’s boundaries is known as the parallelogram’s perimeter. The length and breadth of a parallelogram must be determined in order to determine its perimeter. Let a and b make up the parallelogram’s sides. Considering the parallel and congruent nature of the opposite sides, a parallelogram’s characteristic. A parallelogram’s perimeter is determined by:

Perimeter: a + b + c + d (when a, b, c, d are representing 4 sides of a parallelogram)

Side BC = AD = a because side AB = CD = b.

A parallelogram’s perimeter equals 2 (a + b).

### Example on Parallelogram Formula

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