Properties of Quadrilaterals

Question

https://e-gmat.com/blogs/wp-content/uploads/2019/07/quadrilaterals-properties-formaulas-classification-polygon-four-sided.jpg

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.

https://e-gmat.com/blogs/wp-content/uploads/2019/07/q1.png

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.

https://e-gmat.com/blogs/wp-content/uploads/2018/07/FT-header3-e1532524244114.jpg

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

https://e-gmat.com/blogs/wp-content/uploads/2019/07/q2.png

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)

https://e-gmat.com/blogs/wp-content/uploads/2019/07/q3.png

https://e-gmat.com/blogs/wp-content/uploads/2018/07/FT-header3-e1532524244114.jpg

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

https://e-gmat.com/blogs/wp-content/uploads/2019/07/q4.png

https://e-gmat.com/blogs/wp-content/uploads/2019/07/q5.png

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

https://e-gmat.com/blogs/wp-content/uploads/2018/07/FT-header3-e1532524244114.jpg

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

https://e-gmat.com/blogs/wp-content/uploads/2019/07/q6.png

Formulas to remember   
 https://e-gmat.com/blogs/wp-content/uploads/2019/07/q7.png

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

https://e-gmat.com/blogs/wp-content/uploads/2018/07/FT-header3-e1532524244114.jpg

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

https://e-gmat.com/blogs/wp-content/uploads/2019/07/q8.png

https://e-gmat.com/blogs/wp-content/uploads/2019/07/q9.png

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

https://e-gmat.com/blogs/wp-content/uploads/2018/07/FT-header3-e1532524244114.jpg

Trapezium

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

https://e-gmat.com/blogs/wp-content/uploads/2019/07/q10.png

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

https://e-gmat.com/blogs/wp-content/uploads/2018/07/FT-header3-e1532524244114.jpg

Summary of all the properties we learnt

https://e-gmat.com/blogs/wp-content/uploads/2019/07/q11.png

https://e-gmat.com/blogs/wp-content/uploads/2016/12/Geometry-Ability-Quiz-4-e1480581478957.png

dine5207 · Answer

Practice test is missing  EgmatQuantExpert  and great article though

EgmatQuantExpert · Answer

Hey  dine5207 ,
Glad that you liked the article.

We will update the quizzes link soon in the article.

Regards,
Ashutosh

EgmatQuantExpert · Answer

Hey Everyone, Here is a list of questions specifically designed to help you apply the learnings from this article. Exercise Questions Question 1 Question 2 Detailed solutions will be posted soon. Happy Learning!

https://e-gmat.com/blogs/wp-content/uploads/2018/08/Quant-workshop_Webinar-e1533628475738.jpg

EgmatQuantExpert · Answer

Hey everyone,

The answers to the practice questions have been posted.

Regards,
e-GMAT

howardellis · Answer

Even though there is a clear way to do it, I still get the parallelogram formula wrong
Need a mnemonic solution for this  io games

alishakihn · Answer

Best article of the day I read, I appreciate you sharing this information. I will visit your website often.

alishakihn · Answer

Best article of the day I read, I appreciate you sharing this information. I will visit your website often.

Properties of Quadrilaterals

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Properties of Quadrilaterals

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