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.

Table of Contents:

• Definition
• Types
• Formula
• Quadrilateral Properties
• Summary
• Notes
• Examples
• FAQs

Quadrilateral Definition

A quadrilateral is a plane figure that has four sides or edges, and also have 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:

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

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 or crossed quadrilaterals

The images of these quadrilaterals are given below:

Quadrilateral Formula

Area of the quadrilateral is the total space occupied by the figure. The area formula for the different quadrilaterals are given below:

Quadrilateral Properties

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

• Four sides: AB, BC, CD, and DA
• Four vertices: Points A, B, C, and D
• Four angles: ∠ABC, ∠BCD, ∠CDA, and ∠DAB
• ∠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

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

Square Properties

• All the sides of the square are of equal measure
• The sides are parallel to each other
• All the interior angles of a square are at 90 degrees (i.e., right angle)
• The diagonals of a square perpendicular bisect each other

Rectangle Properties

• The opposite sides of a rectangle are of equal length
• The opposite sides are parallel to each other
• All the interior angles of a rectangle are at 90 degrees.
• The diagonals of a rectangle bisect each other.

Rhombus Properties

• All the four sides of a rhombus are of the same measure
• The opposite sides of the rhombus are parallel to each other
• The opposite angles are of the same measure
• The sum of any two adjacent angles of a rhombus is equal to 180 degrees
• The diagonals perpendicularly bisect each other

Parallelogram Properties

• The opposite side of the parallelogram are of the same length
• The opposite sides are parallel to each other
• The diagonals of a parallelogram bisect each other
• The opposite angles are of equal measure
• The sum of two adjacent angles of a parallelogram is equal to 180 degrees

Properties of Trapezium

• Only one pair of the opposite side of a trapezium is parallel to each other
• The two adjacent sides of a trapezium are supplementary (180 degrees)
• The diagonals of a trapezium bisect each other in the same ratio

Properties of Kite

• The pair of adjacent sides of a kite are of the same length
• The largest diagonal of a kite bisect the smallest diagonal 
• Only one pair of opposite angles are of the same measure.

Summary of Quadrilateral Properties

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, in which 2 pairs of adjacent sides are equal to each other.

Quadrilaterals Examples

Example 1: What is the base of a rhombus, if its area is 40 square units and the height is 8 units?
Solution:
Given,
Area = 40 square units
Height = 8 units
Area of rhombus = Base × Height
40 = Base × 8
Base = 40/8 = 5 units
Example 2: If 15 metre and 6 metres are diagonal lengths of a  kite, then what is its area?

Solution: Given, diagonal 1 = 15 metre and diagonal 2 = 6 metre. So, the area is simply calculated as, (1/2)(15×6) = 45 m².

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

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