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Quadrilaterals

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Quadrilaterals


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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.

As you progress through this article, you will get the chance to test your learnings by attempting two quizzes.
    A.Quiz - 1: This is a pre-quiz. You can take this quiz to check your current knowledge of quadrilateral and its properties.
    B.Quiz 2: This is a post-quiz that will check your understanding once you have read the article.

So, lets 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.

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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.

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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

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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)

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Square

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

    Diagonals bisect each other perpendicularly

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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


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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 \(180^o\)

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Formulas to remember
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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

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Rhombus

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

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

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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 = \(\frac{1}{2} d_1 d_2\)


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Trapezium

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

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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

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Summary of all the properties we learnt

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