Introduction

A closed, four-sided polygon having four vertices and four angles is known as a quadrilateral. A quadrilateral's internal angles are always added up to 360 degrees. Based on the length and angles of their sides, quadrilaterals may be divided into numerous varieties, including squares, rectangles, parallelograms, trapezoids, and rhombuses. Depending on how their angles are oriented, they can also be categorized as convex or concave. In geometry and practical contexts including design, engineering, and architecture, quadrilaterals are often employed.

What is a Quadrilateral?

A polygon with four sides, four angles, and four corners is called a quadrilateral. To put it another way, a quadrilateral is a closed shape that is created by joining together four points, three of which are not on the same line. The quadrilateral's interior angles add up to 360 degrees. A quadrilateral may or may not have equal sides on all four sides.

Types of Quadrilaterals

Based on their characteristics, such as the length and angle of their sides, quadrilaterals may be classified into several categories.

• All of a square's sides are equal in length, and all of its inner angles are 90 degrees.

• Although a rectangle can have various side lengths, it has four right angles.

• A rhombus has all of its sides of equal length, whereas a parallelogram has two sets of parallel sides.

• One pair of parallel sides and non-parallel sides of various lengths make up a trapezium.

• Kites, which have two pairs of adjacent sides of equal length and one pair of non-adjacent sides of equal length, and irregular quadrilaterals, which do not fall into any of the previous categories, are examples of additional forms of quadrilaterals.

Properties of Quadrilaterals

Each of the quadrilaterals described above has its own properties. However, there are some properties that all quadrilaterals have in common. They are:

• The sum of the internal angles, which is always equal to 360 degrees, is one of a quadrilateral's characteristics. 

• A parallelogram also has opposite sides that are parallel and congruent, as well as opposed angles that are equal. 

• Four right angles and opposing sides that are parallel and congruent define a rectangle. 

• Every side of a square is the same length, and every angle is 90 degrees. 

• A trapezium contains one pair of parallel sides and non-parallel sides of various lengths, whereas a rhombus has all of its sides being the same length.

Square Properties  

• A square has four sides that are all of the same length.

• A square's four inner angles are all right angles. (90 degrees).

• A square's opposing sides are congruent and parallel.

• A square's diagonals are equal in length and bisect one another.                                                                     

Rectangle Properties

• A rectangle's opposite sides are parallel and congruent.

• A rectangle's four inner angles are all right angles. 

• A rectangle's diagonals are congruent and cut in half.

• To get a rectangle's area, multiply its length by its width. (l x w).

Rhombus Properties                                                                                       

• A rhombus has four sides that are of the same length.

• A rhombus has parallel and congruent opposite sides.

• A rhombus's diagonals are at right angles to one another.

• Calculating a rhombus's area requires multiplying one diagonal length by the other's, then dividing the result by two (d1 x d2 / 2).

Parallelogram Properties                                                                                 

• A parallelogram's opposite sides are parallel and congruent.

• A parallelogram has congruent, opposite angles.

• A parallelogram's diagonals bisect each other in half.

• The base length and height of a parallelogram are multiplied to determine its area. (b x h).

• The lengths of all four sides of a parallelogram are added to determine its perimeter.

Properties of Trapezium

• One pair of parallel and one pair of non-parallel sides make up a trapezium.

• The angles on each side of the parallel sides are supplementary (add up to 180 degrees).

• A trapezium's diagonals intersect one another.

• The median's length, which connects the non-parallel sides' midpoints, is the same as the average length of the parallel sides.

Properties of Kit

• Two adjacent side pairs with the same length.

• Angles that are opposite one another are congruent.

• A kite's diagonals bisect one another at a 90-degree angle.

• The lengths of the two diagonals are multiplied and divided by two to determine a kite's area (d1 x d2 / 2).

Improtant Quadrilateral Formulas

There are two basic formulas used for a quadrilateral.

Solved Examples

Q1. The perimeter of a square is 20 cm. What is the length of each side?

Solution: The lengths of all sides of a square are added to determine its perimeter.

We know that the Perimeter of a Square = 4 X Side

           Now put perimeter = 20 cm 

         20 =4 X Side

Hence the length of each side of a given square is 5 cm.

2. What is the area of a rectangle that measures 15 meters long by 7 meters wide?

Solution: To get a rectangle's area, multiply its length by its width. 

As a result, this rectangle has a surface area of 15 x 7 = 105 square meters.

3. The diagonals of a rhombus are 6 cm and 8 cm long. What is its area?

Solution: The lengths of the two diagonals are multiplied and divided by two to determine the area of a rhombus. 

Therefore,

Summary

In geometry, a quadrilateral is a closed shape formed by connecting four points, three of which are not on the same line. A quadrilateral has 4 sides, and four 4, and four corners. The sum of all the interior angles of a quadrilateral is 360 degrees. All four sides of a quadrilateral may or may not be equal.

Frequently asked question

Q1. What distinguishes a parallelogram from a rhombus?

A rhombus is a quadrilateral with all of its sides being the same length, whereas a parallelogram is a quadrilateral with two sets of parallel and congruent sides. So a rhombus is a particular kind of parallelogram.

Q2. What characteristics make a quadrilateral a square?

A sort of quadrilateral with all sides being the same length and all angles being 90 degrees is a square. Therefore, you may measure a quadrilateral to make sure all of its sides are the same length and all of its angles are right angles to see whether it is a square.

Q3. What do convex and concave quadrilaterals mean?

The definition of a convex quadrilateral is a quadrilateral whose two diagonals are entirely enclosed inside the figure. Contrarily, a concave quadrilateral has at least one diagonal that extends partially or completely outside of the figure.