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Properties of Quadrilaterals

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Properties of Quadrilaterals  [#permalink]

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New post Updated on: 23 Jul 2019, 23:47
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Properties of Quadrilaterals


Image


Purpose of the article:

Hello Reader,

I see that you are looking to know about various types of quadrilaterals.
    • Well, you have landed just at the right place.

In this article,
    • You will get an idea about the quadrilateral and its various types.
    • You will also get to know about the properties of a few special kinds of quadrilaterals.

So, let’s get straight into it.

What is a quadrilateral?

A quadrilateral is a polygon that has 4 sides.
    • So, any closed figure that has 4 sides is a quadrilateral.
    • And, all the angles of a quadrilateral sum up to 3600.

The diagram given below shows a quadrilateral ABCD and the sum of its internal angles.

Image

Various kinds of quadrilateral

There are some special kinds of quadrilateral that we see in our textbooks/ exams.
These are:
    1. Rectangle
    2. Square
    3. Rhombus
    4. Parallelogram
    5. Trapezium

Let us discuss each type in detail.

Image



Rectangle

A rectangle is a quadrilateral:
    • Each of the 4 angles are \(90^o\)
    • And, opposite sides of a rectangle are equal and parallel
    • Diagonals of a rectangle bisect each other

Image

Formulas to remember

If the length of the rectangle is L and breadth is B then,
    1. Area of a rectangle = Length × Breadth or L × B
    2. Perimeter of rectangle = 2 × (L + B)

Image

Image



Square

A square is a quadrilateral:
    • That has all the angles as \(90^o\)
    • All sides of a square are equal
      o And, opposite sides are parallel to each other

    • Diagonals bisect each other perpendicularly

Image

Image


Formulas to remember

If the side of a square is “a” then,
    1. Area of the square = \(a × a = a^2\)
    2. Perimeter of the square = 2 × (a + a) = 4a


Image




Parallelogram

A parallelogram is a quadrilateral in which:
    Opposite angles are equal
    Opposite sides are equal and parallel
    • Diagonals bisect each other
    • Sum of any two adjacent angles is \(180^o\)

Image


Formulas to remember
Image

If the length of a parallelogram is “l”, breadth is “b” and height is “h” then:
    1. Perimeter of parallelogram= 2 × (l + b)
    2. Area of the parallelogram = l × h

Image



Rhombus

A rhombus is a quadrilateral in which:
    Opposite angles are equal
    All sides are equal
      o And, opposite sides are parallel to each other

    Diagonals bisect each other perpendicularly
    • Sum of any two adjacent angles is \(180^o\)

Image

Image


Formulas to remember

    If the side of a rhombus is a then,
      Perimeter of rhombus= 4a

    If the length of two diagonals of the rhombus is d1 and d2 then:
      Area of the rhombus = \(\frac{1}{2} × d_1 × d_2\)


Image



Trapezium

A trapezium is a quadrilateral in which:
    • Only one pair of opposite sides are parallel to each other

Image


Formulas to remember

    If the height of a trapezium is “h” (as shown in the above diagram) then:
      Perimeter of the trapezium= Sum of lengths of all the sides = AB + BC + CD + DA
      Area of the trapezium = \(\frac{1}{2}\) × (Sum of lengths of parallel sides) × h
      = \(\frac{1}{2}\)× (AB + CD) × h

Image


Summary of all the properties we learnt

Image


Image
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Originally posted by EgmatQuantExpert on 10 Jul 2019, 01:00.
Last edited by EgmatQuantExpert on 23 Jul 2019, 23:47, edited 2 times in total.
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Re: Properties of Quadrilaterals  [#permalink]

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New post 16 Jul 2019, 23:04
Practice test is missing EgmatQuantExpert and great article though
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Re: Properties of Quadrilaterals  [#permalink]

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New post 18 Jul 2019, 03:18
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Re: Properties of Quadrilaterals  [#permalink]

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New post 23 Jul 2019, 03:07
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New post 25 Jul 2019, 01:05
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Re: Properties of Quadrilaterals   [#permalink] 25 Jul 2019, 01:05
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