Quadrilateral

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 is as given below.

  1. concave quadrilaterals
  2. convex quadrilaterals
  3. intersecting quadrilaterals

The images of these are as 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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Practise This Question

Identify the number of triangles in the given figure:

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