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

Students who need to make a personal note about the Parallelogram Formula can consult the examples offered by the subject matter experts on the Extramarks website. The website’s offered Parallelogram Formula allows for self-study and can be used for review. One of the best tools for helping students prepare for their board exams is the Parallelogram Formula offered at Extramarks. The examples of the Parallelogram Formula that are supplied by Extramarks must be continuously practiced by students if they want to perform well on their board examinations. For a quick review, Extramarks’ Parallelogram Formula examples are really helpful. If the Parallelogram Formula examples are not appropriately presented in steps, students may find it difficult to understand them. Therefore, the subject matter experts at the Extramarks website created every example with step-by-step solutions that help students understand the concept easily. The Extramarks platform is used as an illustration to show how technology can increase the effectiveness and clarity of the educational process.

The Extramarks website provides examples of the Parallelogram Formula to help students. The Extramarks organization is dedicated to ensuring students’ growth and prosperity in order to encourage academic achievement. Students occasionally struggle with the Parallelogram Formula, therefore, the website provides step-by-step examples to the students who are registered with its website. Students may access the whole curriculum coverage through Extramarks, ensuring they will perform well in any in-school or annual exams. In order to eliminate the need for students to turn elsewhere for review, Extramarks offers them a learning experience that is aligned with the curriculum. Students must select Extramarks as their study partner in order to receive great grades since Extramarks connects them with skilled professionals who are subject matter experts that strengthen the students’ basic concepts. The concerns of the students related to any particular topic or issue are addressed by the experts at the Extramarks’ website. Extramarks’ professionals are highly qualified and skilled in guiding students to success.

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FAQs (Frequently Asked Questions)

1. Which geometric shape is a parallelogram?

A parallelogram is a square. It is always the case. Quadrilaterals with four congruent sides, four right angles, and two sets of parallel sides are called squares. Quadrilaterals having two sets of parallel sides are known as parallelograms.

2. Why does the area of a parallelogram work?

A parallelogram’s area is determined by multiplying its length by its height. A quadrilateral’s interior angles add up to 360 degrees. Two pairs of parallel sides with equal lengths make up a parallelogram. Its area and perimeter are defined by the fact that it is a two-dimensional figure.

3. What practical use do parallelograms have?

Two parallel, equally long side pairs comprise a rectangle table. As a result, a rectangular is also a parallelogram.As a result, rectangular tables are an everyday example of a parallelogram-shaped object. There are parallelograms on many types of stationery and school supplies.