The Ultimate Reference to What is a Quadrilateral: Definition, Properties, Types, Formulas

Despite being one of the most popular shapes that have been used all around us, many are not aware of exactly what is a quadrilateral.  This blog is your go-to resource to know everything about it effortlessly. Read further and demystify all your doubts.

A closed quadrilateral has four sides, four vertices, and four angles. It's a type of polygon. To make a quadrilateral, we connect four points that are not in a straight line. The total interior angle of a quadrilateral is always 360 degrees.

The English word "quadrilateral" comes from the Latin words "quadra," meaning four, and "latus," meaning sides. Not all quadrilaterals have identical sides. This means we can have different types of quadrilaterals depending on the lengths and angles of the sides.

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So, let’s dig deeper into all the important related to the topic.

Definition of a Quadrilateral:

A quadrilateral is a closed figure having four sides, four vertices, and four angles. By joining four points that are not in a straight line, we can create a quadrilateral. A quadrilateral's angles together make 360 degrees in total.

Each of a quadrilateral's four corners is referred to as a vertex. Consider the ABCD quadrilateral as an example. A, B, C, and D are the angles at the vertices of ABCD. AB, BC, CD, and DA are the other four sides of the quadrilateral.

We combine the opposing vertices of a quadrilateral to determine its diagonals. The diagonals AC and BD for the quadrilateral ABCD as shown in the figure above.

With the definition of the topic clear to you now, let’s go through the types of quadrilaterals.

Types of a Quadrilateral

Quadrilateral types are determined by measuring the angles and side lengths. These designs have four sides since the term "quad" indicates "four," and their angles add up to 360 degrees. Here are the diverse kinds of quadrilaterals:

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

There is another way to classify quadrilaterals with respect to diagonals’ intersection:

Convex Quadrilaterals:

In a convex quadrilateral, both diagonals are entirely inside the figure.

Concave Quadrilaterals:

 In a concave quadrilateral, at least one diagonal is partially or completely outside the figure.

Intersecting Quadrilaterals:

Intersecting quadrilaterals are not simple quadrilaterals. They have a pair of non-adjacent sides that intersect. These types of quadrilaterals are also called self-intersecting or crossed quadrilaterals.

Formula and Properties of a Quadrilateral

We can acquire a more exhaustive understanding of the concept by utilizing an illustration.

• Its sides are AB, BC, CD, and DA.
• There are four of them: Indicators A, B, C, and D.
• The angles are ABC, BCD, CDA, and DAB.
• Angles A and B are proximate to each other.
• The polar opposing angles are A and C.
• AB and CD are two opposing sides.
• The adjoining sides are AB & BC.

A 4-sided plane formation is called a quadrilateral. The following are some critical aspects of quadrilaterals:

• There are four vertices, four angles, and four sides of every figure considered as a quadrilateral.
• Its inner angles add up to 360 degrees.

Formula and Properties of a Square

1. Formula

L2 is the square of the length, where L is the length.

Area = L2.

4L is the perimeter.

2. Properties

• The square's sides are identical.
• The inner angles of a square are perpendicular, and the sides are parallel.
• A square's diagonals are divided at right angles by one another.
• Directly across from each other are the two sides.
• Aligned diagonals are present.
• There are two parallel, divided diagonals.
• A square is a parallelogram with the same angles and sides.
• A parallelogram also turns into a square when its diagonals and right bisectors are equal.

Formula and Properties of a Rectangle

1. Formula

The diagonal length is (L2 + B2), where L means length and B for breadth.

Area equals L * B

Perimeter equals 2(L + B).

2. Properties

• In a rectangle, the opposite sides are identical.
• A rectangle's internal angles are at right angles, and its opposite sides are parallel.
• A rectangle's diagonals bisect each other in two equal parts.
• The opposing sides are congruent and parallel.
• Each factor is appropriate.
• The diagonals divide one another in an equal and congruent way.
• Congruent averse angles are formed at the junction of diagonals.
• A rectangle is a specific kind of parallelogram whose angles are at right angles to one another.

Formula and Properties of a Rhombus

1.    Formula

If a and b are a rhombus's diagonal lengths, then.

Perimeter = 4L, Area = (a*b) / 2.

2.    Properties

• All four sides of a rhombus are the same size.
• The rhombus's averse sides are parallel, and its opposing angles are identical.
• Any two neighboring angles in a rhombus together add up to 180 degrees.
• The diagonals divide each other in half perpendicularly.
• The angles are all alike.
• Contrary angles are congruent angles.
• The diagonals split in half and are parallel.
• A rhombus is nothing but a parallelogram whose diagonals are parallel.

Formula and Properties of a Parallelogram

• The parallelogram's averse side equals its other side.
• Both sides are parallel.
• A parallelogram's diagonals divide each other into equal parts.
• The opposite angles are the same.
• A parallelogram's two adjoining angles’ addition is 180 degrees.

Properties of a Trapezium

A trapezium is a polygon with a set of parallel sides. These sides are also known as the parallel sides of a trapezium. The other two sides of trapezoids, commonly referred to as their legs, are unparallel.

• A trapezium only has one duo of opposing sides that are parallel.
• A trapezium's two adjacent sides are 180-degree supplementary.
• The diagonals of a trapezium divide one another in the same ratio.
• A trapezium's bases are parallel.
• There are no sides, angles, or diagonals in a trapezium.
• A trapezium is a closed, quadrilateral shape with a boundary encompassing a specific area.
• Parallel sides are the bases of a trapezium.
• The non-parallel sides are considered as legs or lateral sides.
• The distance between parallel sides is known as the height.

Properties of a Kite

Two consecutive pairs of congruent sides that are near to one another and have the same length each make up a quadrilateral known as a kite.

Properties:

• The two angles are the same where the unequal sides join.
• It can be visualized as the base of two congruent triangles.
• Two of its diagonals cross at a right angle to one another.
• The longer or major diagonal divides the other diagonal.
• The primary diagonal of a kite is proportional.
• The kite is composed of two isosceles triangles of equal size, each separated by a diagonal of equal size.
• A kite's two adjoining sides are the same.
• A kite's largest and smallest diagonals are bisected equally.
• The dimensions of only one pair of opposing angles are identical.

Other Categories of Quadrilaterals

1. Isosceles Trappezoid

An isosceles trapezium is a figure with non-parallel sides and similar base angles. Put differently, if a trapezoid's two bases are parallel and its other two sides that are not parallel are identical in length, the trapezoid is isosceles.

Properties

• It has an axis of symmetry. There is no rotational symmetry, and there is only one line of symmetry joining the centers of the parallel sides.
• In an isosceles trapezoid, the bases' sides are parallel to each other.
• Except for the base, all the other sides are non-parallel and of identical length.
• The diagonals are equal, and the base angles are similar.
• 180° is a complement to the opposite angle.
• The centers of the parallel sides are connected by a line element perpendicular to the bases.

Formula

• Area = (sum of parallel sides ÷ 2) × h
• Perimeter = sum of all sides

2. Cyclic Quadrilateral

A quadrilateral whose four vertices are all set on a circle is referred to as a cyclic quadrilateral. It is also directed to a carved quadrilateral. The circle with every vertex of each polygon along its perimeter is comprehended as a circumnavigated circle.

Properties

• In a cyclic quadrilateral, the total of two opposite angles is 1800(supplementary).
• If the addition of two opposing angles is more than one, the quadrilateral becomes cyclic.
• The four vertices of a cyclic quadrilateral are at the circumference of a circle.
• To create a parallelogram or rectangle, just join the midpoints of the four sides in decreasing order.
• An external angle equal to the inner angle on the opposite side is produced when a cyclic quadrilateral is formed.

Conclusion

Quadrilaterals are one of the most basic topics in mathematics. If you're studying for exams involving area and perimeter concepts, becoming familiar with quadrilaterals is important. They are not only relevant in degree courses but also in everyday objects like picture frames, table tops, doors, and books.

In fact, you'll discover quadrilaterals in almost every facet of daily life. Such crucial topics are often used as assignment subjects. If you face difficulties writing a paper on such a topic, you can look for assignment help online.

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