Quadrilateral

What is a Quadrilateral? 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 like rectangle, square, trapezoid, and kite or irregular and uncharacterized as shown below:

Quadrilateral
Types of Quadrilaterals

Types Of Quadrilaterals

  • 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.

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

Properties of Quadrilateral

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
Types of Quadrilateral

Types of Quadrilaterals

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

Quadrilateral

  • Four side: 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

Area of Quadrilateral

What is area of 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

Examples on Quadrilaterals:

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. Answer!

 

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 mtr

So area is simply calculated as, 1/2(15×6) = 45 square mtr.

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Practise This Question

ABCD is a parallelogram in which DCB and ABC are in ratio 2:7. Find the sum of ABD and ADB.