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# Properties of Quadrilaterals

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Joined: 04 Jan 2015
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Updated on: 23 Jul 2019, 23:47
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Purpose of the article:

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

• 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.

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.

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

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)

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

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

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 $$180^o$$

Formulas to remember

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

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 $$180^o$$

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 = $$\frac{1}{2} × d_1 × d_2$$

Trapezium

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

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

Summary of all the properties we learnt

_________________

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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Joined: 21 Oct 2018
Posts: 32
Location: India

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16 Jul 2019, 23:04
Practice test is missing EgmatQuantExpert and great article though
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3134

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18 Jul 2019, 03:18
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23 Jul 2019, 03:07
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25 Jul 2019, 01:05
Re: Properties of Quadrilaterals   [#permalink] 25 Jul 2019, 01:05
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# Properties of Quadrilaterals

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