Quadrilateral

In Geometry, the shapes or objects are classified based on the number of sides. The different classification of shapes are:

  • Triangle ( 3-sides)
  • Quadrilateral (4-sides)
  • Pentagon (5-sides)
  • Hexagon (6-sides)
  • Heptagon (7-sides)
  • Octagon (8-sides) and so on.

In this article, we are going to discuss “Quadrilaterals” in detail.

Quadrilateral Definition

A quadrilateral is a plane figure that has four sides or edges, so having four corners or vertices. Quadrilaterals will typically be of standard shapes with four sides like rectangle, square, trapezoid, and kite or irregular and uncharacterized as shown below:

Quadrilateral

Types of Quadrilaterals

There are many types of quadrilaterals. As the word ‘Quad’ means four, all these types of a quadrilateral have four sides and the sum of angles of these shapes is 360 degrees.

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

Types Of Quadrilaterals

Another way to classify the types of quadrilaterals are:

  1. Convex Quadrilaterals: Both the diagonals of a quadrilateral are completely contained within a figure.
  2. Concave Quadrilaterals: At least one of the diagonals lies partly are entirely outside of the figure.
  3. Intersecting Quadrilaterals: Intersecting quadrilaterals are not simple quadrilaterals in which the pair of non-adjacent sides intersect. This kind of quadrilaterals are known as self-intersecting quadrilaterals.

The images of these quadrilaterals are given below:

different types of quadrilaterals

Quadrilateral Properties

A quadrilateral is a 4-sided plane figure. Below are some important properties of quadrilaterals :

  • Every quadrilateral has 4 vertices, 4 angles, and 4 sides
  • The total of its interior angles = 360 degrees
  • A quadrilateral with four equal sides and four right angles is a square
  • A quadrilateral that has opposite sides equal and measure of every angle is 90 degrees is a rectangle
  • Parallelogram, trapezium, rhombus, and kite are other examples of quadrilaterals

Quadrilateral Properties chart

Let us understand in a better way with the help of an example:

Quadrilateral

  • Four sides: AB, BC, CD, and DA
  • Four vertices: Points A, B, C, and D
  • Four angles: ∠ABC, ∠BCD, ∠CDA, and ∠DAC
  • ∠A and ∠B are adjacent angles
  • ∠A and ∠C are the opposite angles
  • AB and CD are the opposite sides
  • AB and BC are the adjacent sides

Quadrilateral Formula

What is the area of the quadrilateral?

Area of the quadrilateral is the total space occupied by the figure. There are different types of quadrilaterals. Let us study area formula each of them:

Area of a Parallelogram Base x Height
Area of a Rectangle Length x Width
Area of a Square Side x Side
Area of a Rhombus 1/2 x Diagonal 1 x Diagonal 2 OR  Base x Height
Area of a Kite 1/2 x Diagonal 1 x Diagonal 2

Quadrilaterals Examples

Example 1: What is the base of a rhombus? If its area=40 and the height is 8.

Solution: Area=40, and height= 8 (Given)

Area of rhombus=base x height base = 40/8 = 5. 

Example 2: If 15 mtr and 6 mtr are diagonal lengths of a  kite, then what is its area?

Solution: Given, diagonal 1 = 15 mtr and diagonal 2 = 6 mtrSo area is simply calculated as, 1/2(15×6) = 45 square mtr.

You can practice more examples of Quadrilateral using the quadrilateral worksheet.

Notes on Quadrilateral

  • A quadrilateral is a trapezoid or a trapezium if 2 of its sides parallel to each other.
  • A quadrilateral is a parallelogram if 2 pairs of sides parallel to each other.
  • Squares and Rectangles are special types of parallelograms. Below are some special properties.– All internal angles are of “right angle” (90 degrees).– Each figure contains 4 right angles.– Sides of a square are of the same length (all sides are congruent) – Opposite sides of a rectangle are same.– Opposite sides of a rectangle and square are parallel.
  • A quadrilateral is a rhombus, if
    • All the sides are of equal length-Specified 2 pairs of sides are parallel to each other.
  • A kite is a special sort of quadrilateral, wherever 2 pairs of adjacent sides are equal to each other.

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Frequently Asked Questions

What are Quadrilaterals and its types?

A quadrilateral can be defined as a plane figure having 4 sides. There are mainly 6 types of quadrilaterals which are:

  • Trapezium
  • Parallelogram
  • Rectangle
  • Rhombus
  • Square
  • Kite

Apart from these 6 types, a quadrilateral can also be classified as:

  • Concave quadrilaterals
  • Convex quadrilaterals
  • Intersecting quadrilaterals

What is convex and concave quadrilateral?

A convex quadrilateral can be defined as a quadrilateral whose both the diagonals are completely contained within the figure. On the other hand, a concave quadrilateral is a quadrilateral which is having at least one diagonal that lies partly or entirely outside of the figure.

What is the sum of the interior angles of a quadrilateral?

The sum of all the interior angles of a quadrilateral is 360°.

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