Categories: Class 10

# What is Quadrilateral? Definition,Types, Properties, Examples

A polygon with four sides, four angles, and four vertices is called a quadrilateral. As suggested by the name, it always has four sides, four angles, and four vertices. The quadrilateral has angles at each of its four vertices, or corners. The sum of 4 angles is always 360 degrees. In the below figure.ABCD is a quadrilateral.

• The quadrilateral ABCD’s four angles are ∠A, ∠B, ∠C, and ∠D
• The four sides of the quadrilateral ABCD are AB, BC, CD, and DA.
• The quadrilateral ABCD’s four vertices are A, B, C, and D.
• The quadrilateral ABCD’s two diagonals are AC and BD.

A quadrilateral is a two-dimensional shape that has four sides, four angles, and four vertices.A quadrilateral does not always have to have equal lengths on each of its four sides. As a result, depending on the sides and angles, we have several types of quadrilaterals. There are four different types of quadrilaterals: There are many different types of quadrilaterals, such as

1. Trapezium
2. Parallelogram
3. Squares
4. Rectangle
5. Rhombus
6. Kite

The following quadrilaterals each have unique characteristics. Nevertheless, all quadrilaterals have a few characteristics. They are listed below.

2. They have four vertices.
3. There are two diagonals in each
4. They have four interior angles.
5. The Sum of all interior angles of a quadrilateral is 360°

The basic classification of the quadrilaterals is between convex and concave quadrilaterals. Types of quadrilaterals are separated into different groups based on their properties. These quadrilaterals that are concave and convex can be divided further into their subgroups.

Concave Quadrilaterals: Concave quadrilaterals are polygons with four sides and an interior angle larger than 180. A convex quadrilateral’s two diagonals are included in the enclosed figure.A Dart is an example of a concave quadrilateral.

Convex Quadrilaterals: A four-sided polygon with inner angles that are less than 180 degrees each is referred to as a convex quadrilateral. Squares, rectangles, parallelograms, rhombuses, kites, and trapezoids are examples of convex quadrilaterals (trapezium).

## Types of Quadrilaterals and its Properties

Let’s take a look at the various types of quadrilateral and their properties with the figure.

### Parallelogram

A quadrilateral with two sets of parallel sides is known as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size.

Properties of Parallelogram:

• The opposing sides are equal and parallel.
• Angles on either side are equal.
• The two diagonals of the parallelogram are split in two.
• The parallelogram is divided into two congruent triangles by each diagonal.
• A parallelogram’s total square sum and the total square sum of its diagonals are equivalent. Also known as the parallelogram law.

### Rhombus

A rhombus is a quadrilateral with opposite sides that are parallel to one another and equal opposite angles. A rhombus has equal lengths on all sides, making it an equilateral quadrilateral.

Properties of Rhombus:

• A rhombus has an equal number of sides.
• Every Rhombus has two diagonals that join the opposite vertices in pairs.
• A rhombus’ diagonals will always cut each other at a 90-degree angle.
• A rhombus is divided into four right-angled congruent triangles by its two diagonals.
• Any two parallel or following angles added together equal 180 degrees.

### Trapezium

The trapezium is a quadrilateral in two dimensions with a single pair of parallel opposite sides. The bases and legs of a trapezium are its parallel and non-parallel sides, respectively.

Properties of Trapezium

• A trapezium has four sides, four vertices, and four angles.
•  In A trapezium two parallel sides are known as bases and the other two non-parallel sides are called legs.
• Trapezium has one set of opposite sides which is parallel to the other.
• In a trapezium, the sum of all four internal angles is always 360°.

### Rectangle

A quadrilateral with equal angles and parallel opposite sides is known as a rectangle.Each rectangle shape has two dimensions: length and width.  All of a rectangle’s angles are equal to 90 degrees, and its opposite sides are equal and parallel to one another.

Properties of Rectangle:

• Each of a rectangle’s opposing sides is equal and parallel to the other.
• At each vertex, a rectangle’s inner angle is 90°.
• The sum of all interior angles is 360°.
• Each of the diagonals is divided in half.
• The diagonals are equal in Length

### Square

A quadrilateral with four equal sides is called a square. Equal sides and internal angles that are both 90 degrees distinguish each square shape.

Properties of Square:

• A Square has four sides and four vertices.
• The square’s four sides are equal to one another.
• Each vertex of a square has a 90° internal angle.
• The Sum of all interior angles is 360°.
• A square’s diagonals are parallel to one another.
• The diagonals are all the same length.

### Kite

A kite is a quadrilateral that has two sets of adjacent, equal-length sides. A kite has four vertices, four sides, and four angles.

Properties of Kite

• A kite has two adjacent pairs of equal sides.
• It has a single pair of equal, obtuse, opposite angles.
• In the intersection of the two angles, the two sides are equally sized.
• It has two diagonals that right-angle intersect with one another.
• The diagonals are parallel with one another.
• The longer diagonal splits the two opposing angles in half.
• A kite has symmetry along its main diagonal.

There are two fundamental quadrilateral formulas, which are as follows:

The area of the Quadrilateral refers to the total amount of space that is enclosed by a quadrilateral. Below is a list of the different types of quadrilaterals area formulas:

 Types of Quadrilateral Area Formula Parallelogram Base x Height Rectangle Length x Width Square Side x Side Rhombus (1/2) x Diagonal 1 x Diagonal 2 Trapezium ½ (Sum of parallel sides)(Distance between parallel sides) Kite 1/2 x Diagonal 1 x Diagonal 2

In order to determine the path that encircles a quadrilateral, we must add the lengths and widths of each of its four sides, with lengths being the longest and widths being the shortest. Perimeter is calculated using the formula Perimeter = Length + Length + Width + Width.

Here is a list of Perimeter formulas for different types of quadrilaterals

 Types of Quadrilateral Formula of Perimeter Square 4 x Side Rectangle 2(Length + Breadth) Parallelogram 2(Base + Side) Rhombus 4 x Side Trapezium Sum of all four sides Kite 2 (a + b), a and b are adjacent pairs

A polygon with four sides, four angles, and four vertices is called a quadrilateral. As suggested by the name, it always has four sides, four angles, and four vertices.

A polygon with four sides, four angles, and four vertices is called a quadrilateral. The Latin words Quadri, which means four, and latus, which means side, were combined to create the English word quadrilateral.

The first mathematician to present the formula for the area of a cyclic quadrilateral was Brahmagupta (ad 628) His explanation of how to locate a cyclic quadrilateral with rational sides is the first of its kind.

2. They have four vertices.
3. There are two diagonals in each

## FAQs

A polygon with four sides, four angles, and four vertices is called a quadrilateral. As suggested by the name, it always has four sides, four angles, and four vertices.

### Why are they called quadrilaterals?

A polygon with four sides, four angles, and four vertices is called a quadrilateral. The Latin words Quadri, which means four, and latus, which means side, were combined to create the English word quadrilateral.

The first mathematician to present the formula for the area of a cyclic quadrilateral was Brahmagupta (ad 628) His explanation of how to locate a cyclic quadrilateral with rational sides is the first of its kind.

They have four vertices.
There are two diagonals in each

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