✅ Diagonal of Parallelogram Formula ⭐️⭐️⭐️⭐️⭐

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Diagonal of Parallelogram Formula

Diagonals of a parallelogram formula are used to find the length of the diagonals of a parallelogram. The diagonals of a parallelogram are the connecting line segments between opposite vertices of the parallelogram. Using this formula we can find out the lengths of the diagonals only using the length of the sides and any of the known angles. Let us see more about the diagonals of a parallelogram along with the solved examples in the next section.

What Is the Diagonal of Parallelogram Formula?

The diagonals of a parallelogram formula help calculate the length of the diagonals of a given parallelogram. This formula can be used to find the lengths of the diagonals by using the length of the sides and any of the known angles.

Diagonal of Parallelogram Formula

Formula 1: For any parallelogram abcd, the formula for the length of the diagonals is:

Where,

p and q are the length of the diagionals respectively.
x and y are the sides of the parallelogram.

Formula 2: One more special formula relating the lengths of the diagonals and sides of the parallelogram is:

Where,

p and q are the lengths of the diagonals respectively.
x and y are the sides of the parallelogram.

Let’s take a quick look at a couple of examples to understand the diagonals of the parallelogram formula, better.

Examples using Diagonal of Parallelogram Formula

Example 1: Find the length of the diagonals of the rhombus of side length 4in, if the interior angles are 120°, and 60°.

Solution:

Given, Interior angle A = 120°, and angle B = 60°.
x = 4, y = 4

Using diagonal of parallelogram formula,

Answer: The length of the diagonals are 4 in and 6.92 in.

Example 2: For a parallelogram ABCD, if the length of the adjacent sides is 35 ft and 82 ft. If one of the interior angles is 37°. Find the length of any diagonal.

Solution:

Given, Interior angle A = 37°
x = 35 ft, y = 82 ft

Using diagonal of parallelogram formula,

Answer: The length of the diagonal is 58 ft.

Example 3: Calculate the length of the diagonal of a parallelogram with sides 4 units, 6 units and angle 60 degrees ?

Solution:

Given, a = 4 units, b = 6 units, angle A = 60°

Using diagonal of parallelogram formula,

Answer: Diagonal of parallelogram =;5.291 units.

FAQs on Diagonal of Parallelogram Formula

What Is the Diagonal of a Parallelogram Formula?

The diagonals of a parallelogram formula gives the length of the diagonals of a parallelogram. For any parallelogram abcd, the formula for the lengths of the diagonals are,

How To Use the Diagonal of a Parallelogram Formula?

For any parallelogram, let p and q be the lengths of the diagonals and x and y be the sides of the parallelogram then

Step 1: Check for the given parameters, the values of the sides of the parallelograms, and the corresponding angles.
Step 2: Put the values in the formula,

What Are the Components of the Diagonal of Parallelogram Formula?

The diagonal of parallelogram formula helps to find the lengths of the diagonals by using the length of the sides and any of the known angles. Thus, its components include the sides of the parallelogram and the corresponding angles.

Is the Diagonal of Parallelogram Formula Same For Both the Diagonals?

The diagonal of parallelogram formula for both the diagonals are as follows:

What is a Diagonal?

When students learn about quadrilaterals they get to learn about its various types and names. Quadrilaterals or polygons are geometric figures on a plane with 4 sides, 4 vertices and 4 angles. Depending upon the length of the sides and the degree of angle they form at their joining vertices they have been classified and named differently. The different types of quadrilaterals are as follows :

Square: Having equal sides and angle of 90 degrees it is the most common type and simple quadrilateral that we are all familiar with.

Rectangle: It is similar to square for having equal all 5 angles of 90 degrees but differs due to unequal sides. The opposite sides are equal but adjacent sides are unequal.

Irregular Quadrilateral: It is the most irregular form with unequal sides and angles.

Parallelogram: In a parallelogram the adjacent sides and angles are unequal but opposite sides and angles are equal to each other.

Rhombus: Two sides adjacent to each other are equal in pairs. And only two angles opposite to each other are equal.

Trapezoid or Trapezium: This is a quadrilateral with one pair of sides that are opposite to each other and vary in length and run parallel to each other.

Isosceles Trapezium: It is a special type of Trapezium with the non-parallel sides having an equal length.

These are some of the simple quadrilaterals we have studied in the previous class.

Every quadrilateral has two diagonals that bisect each other at the center of a quadrilateral. Likewise, the diagonals of a parallelogram bisect each other but are not equal in length. Students can easily find out the diagonals of a parallelogram or any other quadrilateral by joining the opposite vertices. In square and rhombus, they always intersect perpendicular to each other while for others it is not perpendicular.

Also note that the longer diagonal is opposite to the larger of the parallelogram’s angles, which is a direct result of the cosine rule.

In the case of a rectangle, which is a type of parallelogram in which the interior angles are 90°, the diagonal formula reduces to the following. The following result can also be obtained by applying the Pythagorean theorem to the rectangle.

Let’s look at the following example to understand how to use these formulas.

Question:

If one of the angles of a parallelogram is 60° and its adjacent sides are 4 cm and 6 cm long, then evaluate the lengths of its diagonals.

Solution:

Why don’t you try to solve the following problem to see if you have mastered these formulas?

Question:

Now, we can solve these two equations to calculate a and b.

Solving this quadratic and ignoring the negative answers (because lengths cannot be negative), we get the following values.

FAQs (Frequently Asked Questions)

1. How to find the length of the diagonals of a quadrilateral?

To calculate and find the length of the diagonals we have to first find out the measure of the sides and angles formed by the sides and the diagonals. Then we can apply the trigonometric rules to find out the length of the diagonals. If the diagonals form a right angle triangle with any two sides of the triangle then the rule of hypotenuse theorem can also be used for finding the length of the diagonal. In some cases the formula for equilateral triangles can also help.

2. How to find out the area of a parallelogram?

Parallelogram is a quadrilateral with one pair of parallel sides. It is different from a rectangular shape because it doesn’t have right-angled corners on its four vertices. So to find out the area covered by the parallelogram you need to find the height or altitude of the parallelogram. after finding out the altitude it is multiplied with the base of the parallelogram. The other method is to first find out the perpendicular distance of the diagonal from one vertice other than the two at its both ends. Then this distance is multiplied with the length of the diagonal to find the area.

3. What are all the types of quadrilaterals studied in higher class math?

Quadrilaterals having four sides and four vertices are classified into two broad categories, simple and complex. Further the simple quadrilaterals can be either concave or convex. Different types of simple convex quadrilaterals are already mentioned. This list also includes oblong, kite, tangential quadrilateral, tangential trapezoid, ex-tangential quadrilateral, cyclic quadrilateral, bicentric quadrilateral, harmonic quadrilateral, orthodiagonal quadrilateral and equi-diagonal quadrilateral. In a concave quadrilateral, one interior angle is bigger than 180 degrees. In such a quadrilateral one diagonal lies outside of the quadrilateral space.

4. How many problem questions on the chapter a student needs to solve for sufficient practice?

The topic on diagonals of parallelogram comes under the chapter of quadrilateral in the higher class Mathematics syllabus. So any student who wants to practice questions to get a good understanding of the chapter can solve the problems provided in the exercises of each chapter. If a student wants more questions then can follow the book of R D Sharma or R S Aggarwal available in the market. Questions are also available on the Vedantu website. Students can download this paper free of cost after they register themselves on the portal.

5. How can I check if my answers to solved questions are correct or not?

Solving problem questions for geometry chapters can be sometimes confusing. It can happen even after you have a clear understanding of the concepts. So it is better to check the Solutions of the questions available and practice better. Vedantu provides all the answers in the form of solutions on its portal for the students preparing by self-studies. The Solutions are available for all popular question sets such as NCERT Textbooks, R D Sharma, R S Aggarwal, and various practice question sets available on this website.

Diagonal of Parallelogram Formula – Definition & Examples

Diagonal of Parallelogram Formula: The name parallelogram comes from the Greek word parallelogrammon, which means bounded by parallel lines. As a result, a parallelogram is a quadrilateral with parallel lines on opposite sides. The opposite sides of a parallelogram will be parallel and equal. The diagonals of a parallelogram are the line segments that connect the parallelogram’s opposite vertices.

We can calculate the lengths of the diagonals of a parallelogram if we know the measure of its adjacent sides and the adjacent angles. In this article, we will discuss the diagonal of the parallelogram formula in detail.

What is a Parallelogram?

A parallelogram is a type of quadrilateral formed by parallel lines. The opposite sides of a parallelogram are parallel and congruent. A parallelogram’s angle between consecutive sides can vary, but the opposite angles are equal.

Examine the diagram below, which represents the three kinds of parallelograms. These are special cases of parallelograms.

Diagonal

A diagonal is a line segment that connects two corners of a polygon that is not an edge. As a result, we may make a diagonal by connecting any two corners (vertices) that are not previously connected by an edge.

Number of Diagonals of a Parallelogram

For an nn -sided regular polygon, the number of diagonals can be obtained using the formula given below:

Diagonals of a Parallelogram

The diagonals of a parallelogram are the line segments joining the opposite vertices of the parallelogram.
A parallelogram has two pairs of opposite vertices, and hence it has two diagonals.

In the parallelogram ABCD, AC and BD are the diagonals.

Diagonals of Parallelogram Formula

The diagonals of a parallelogram formula are used to determine the length of a parallelogram’s diagonals. Using the lengths of the sides and the measure of the angles, we can calculate the diagonal lengths.

Relationship Between Sides and Diagonals of a Parallelogram

Types of Parallelogram

A parallelogram may be classified into several kinds based on its various properties. It is mostly classified into three distinct categories:
1. Rectangle
2. Square
3. Rhombus