Complete Lesson on Quadrilateral: 2022 Update

Various types of shapes vary from each various other in terms of sides or angles. There are numerous shapes with four sides, yet the difference in angles on their sides makes them unique. We call these 4-sided shapes the Quadrilateral.

In this article, you will undoubtedly learn:

What is a quadrilateral?

How the different kinds of quadrilaterals appear?

Additionally, you will learn more about the buildings of quadrilaterals.

What is a Quadrangle?

As words suggest, ‘Quad’ indicates four and ‘side,’ which means side. Consequently, a quadrangle is a closed two-dimensional polygon composed of 4-line segments. In easy words, a quadrangle is a shape with four sides.

Quadrilaterals are everywhere! From the books, chart documents, computer system keys, tv as well as mobile screens. The list of real-life examples of the quadrangle is unlimited.

Sorts of Quadrangles

There are six quadrangles in geometry. Several of the quadrilaterals are indeed acquainted with you, while others might not be so familiar.

Let’s take a look.







A rectangle

A rectangle is a quadrilateral with four appropriate angles (90 °). In a rectangular shape, both the pairs of opposite sides are parallel and equal in length.

Properties of rectangular shapes:

All angles are right angles

The diagonals are congruent.

Rectangular shapes are convenient to have about. For example, shoe boxes, cutting boards, sheets of paper, image frameworks, etc., are all rectangle-shaped.

Rectangles are simple to pile because they have two sets of parallel sides. Their appropriate angles make specific built points such as homes, office complex, colleges, etc., stand straight and tall.

A Square

A square is a quadrilateral with four appropriate angles (90 °). In a square, both pairs of contrary sides are identical as well as equivalent in length.

Characteristic of a square:

All sides of a square are conforming.

All angles are right angles by definition.

Reality– globe examples of squares consist of: computer systems secrets, rollercoasters, rooms on a chessboard etc


It is a quadrilateral with two pairs of the identical opposite as well as equal sides. Furthermore, the opposite angles in a parallelogram are similar in step.

When you look at the parallelogram PQRS, side PQ is parallel to side SR, and side PS is parallel to side QR. Point M is the omphalos of both diagonals of the parallelogram.

For that reason, size PM = MR, & size SM = MQ Rhombus A rhombus is a quadrilateral with all four sides having equivalent sizes. The Reverse sides of a rhombus are equal and identical, and the contrary angles are very same.

ABCD, as we know, is a rhombus in which AB is parallel and equal to DC and AD is also identical and similar to BC.

The diagonals Air Conditioning = BD and also M is the point of crossway of both diagonals.


A trapezium, also known as a trapezoid, is an equilateral with one pair of identical opposite sides. Trapezium sides are also designated as bases, and the vertical line from any vertex of the trapezium to the base is called the elevation.

For instance, ABCD is a trapezium in which side BD is alongside side CA. The vertical line DM is the elevation (h) of the trapezium, while BD and CA are the bases.


The two pairs of side sizes, as well as these sides, are adjacent to each other.

Area of a rhombus

All sides are in agreement necessarily.

The diagonals will bisect the angles.

The diagonals in this shape bisect each other at the best angles.

Feature of Quadrilaterals

The residential properties of quadrilaterals consist of:

Every quadrilateral has four sides, four vertices as well as four angles.4.

The overall action of all the four indoor angles of a quadrangle always amounts to 360 levels.

The value of interior angles of a quadrilateral fits the formula of polygon i.e.

Sum of interior angles = 180 ° * (n– 2), where n amounts to the polygon’s number of sides.

Rectangles, rhombus, and also square are all kinds of parallelograms.

A square is both a rhombus and also a rectangular shape.

The rectangular shape and also rhombus is not square.

A parallelogram is a trapezium.

A trapezium is not a parallelogram.

Kite is not a parallelogram.

Category of quadrangles

The quadrangles are identified right into two fundamental types:

Convex quadrilaterals: These are the quadrangles with interior angles less than 180 degrees, and both diagonals are inside the quadrilaterals. They consist of trapezium, parallelogram, rhombus, rectangular shape, square, kite, etc.

Concave quadrilaterals: These are the quadrangles with at least one indoor angle higher than 180 levels, and also at least one of the two diagonals is outside the quadrangles. A dart is a concave quadrangle.

There is another much less common kind of quadrangles, called facility quadrilaterals. These are crossed figures. For example, went across trapezoid, went across the rectangular shape, went across the square, etc.

Let’s work on a few example problems concerning quadrangles.


The indoor angles of an uneven quadrangle are; x °, 80 °, 2x ° as well as 70 °. Determine the worth of x.


By a building of quadrangles (Sum of interior angles = 360 °), we have,

⇒ x ° + 80 ° + 2x ° +70 °=

360 °.

Streamline. ⇒ 3x + 150 °=

360 °.

Subtract 150 ° on both sides.

⇒ 3x + 150 °– 150 °

= 360 °– 150 °. ⇒ 3x= 210 °. Split both sides by 3 to get;.

⇒ x = 70 °

For that reason, the worth of x is 70 °.