Properties of Quadrilaterals

Properties of Quadrilaterals

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.



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