A 

parallelogram is a two-dimensional geometrical shape, whose sides are parallel to

each other. It is a type of polygon having four sides (also called quadrilateral), where the
pair of parallel sides are equal in length. The Sum of adjacent angles of a
parallelogram is equal to 180 degrees. In geometry, you must have learned about many
2D shapes and sizes such as circle, square, rectangle, rhombus, etc. All of these shapes
have a different set of properties. Also, the area and perimeter formulas of these shapes
vary from each other and are used to solve many problems. Let us learn here the
definition, formulas and properties of a parallelogram.

Table of contents:

 Definition
 Shape
 Special cases
 Angle
 Properties
 Formula
 Types
 Theorems
 Parallelogram and Rhombus
 Examples
 Video Lesson
 FAQs

Parallelogram Definition
A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a
parallelogram are equal in length, and the opposite angles are equal in measure. Also,
the interior angles on the same side of the transversal are supplementary. Sum of all the
interior angles equals 360 degrees.
A three-dimensional shape that has its faces in parallelogram shape, is called a
parallelepiped. The area of parallelogram depends on the base (one of its parallel sides)
and height (altitude drawn from top to bottom) of it. The perimeter of a parallelogram
depends on the length of its four sides.
A square and a rectangle are two shapes which have similar properties of a
parallelogram.
Rhombus: If all the sides of a parallelogram are congruent or equal to each other, then it
is a rhombus.
If there is one parallel side and the other two sides are non-parallel, then it is a
trapezium.
See the figure below:
In the figure above, you can see, ABCD is a parallelogram, where AB || CD and AD ||
BC. 
Also, AB = CD and AD = BC
And, ∠A = ∠C & ∠B = ∠D
Also, ∠A & ∠D are supplementary angles because these interior angles lie on the same
side of the transversal. In the same way, ∠B & ∠C are supplementary angles.
Therefore,
∠A + ∠D = 180
∠B + ∠C = 180

Facts:

 Number of sides = 4
 Number of vertices = 4
 Mutually Parallel sides = 2 (in pair)
 Area = Base x Height
 Perimeter = 2 (Sum of adjacent sides length)
 Type of polygon = Quadrilateral

Shape of Parellelogram
A parallelogram is a two-dimensional shape. It has four sides, in which two pairs of sides
are parallel. Also, the parallel sides are equal in length. If the length of the parallel sides
is not equal in measurement, then the shape is not a parallelogram. Similarly, the
opposite interior angles of parallelogram should always be equal. Otherwise, it is not a
parallelogram.

Special Parallelograms
Square and Rectangle: A square and a rectangle are two shapes which have similar
properties of a parallelogram. Both have their opposite sides equal and parallel to each
other. Diagonals of both shapes bisect each other. 
Rhombus: If all the sides of a parallelogram are congruent or equal to each other, then it
is a rhombus.
Rhomboid: A special case of a parallelogram that has its opposite sides parallel to each
other but adjacent sides are of unequal lengths. Also, the angles are equal to 90
degrees.
Trapezium: If there is one parallel side and the other two sides are non-parallel, then it is
a trapezium. 

Angles of Parallelogram
A parallelogram is a flat 2d shape which has four angles. The opposite interior angles are
equal. The angles on the same side of the transversal are supplementary, that means
they add up to 180 degrees. Hence, the sum of the interior angles of a parallelogram is
360 degrees.

Properties of Parallelogram
If a quadrilateral has a pair of parallel opposite sides, then it’s a special polygon called
Parallelogram. The properties of a parallelogram are as follows:

 The opposite sides are parallel and congruent

 The opposite angles are congruent
 The consecutive angles are supplementary
 If any one of the angles is a right angle, then all the other angles will be at right
angle
 The two diagonals bisect each other
 Each diagonal bisects the parallelogram into two congruent triangles
 The Sum of square of all the sides of parallelogram is equal to the sum of square
of its diagonals. It is also called parallelogram law
Also, read:

 Parallelogram Law
 Diagonal of a Parallelogram Formula
 Important Questions Class 9 Maths Chapter 9 Areas Parallelograms

Formulas (Area & Perimeter)

The formula for the area and perimeter of a parallelogram is covered here in this section.
Students can use these formulas and solve problems based on them.

Area of Parallelogram
Area of a parallelogram is the region occupied by it in a two-dimensional plane. Below is
the formula to find the parallelogram area:
Area = Base × Height

In the above figure, ||gramABCD,  Area is given by;

Area = a b sin A = b a sin B

where a is the slant length of the side of ||gramABCD and b is the base.
Check here: Area of a Parallelogram Formula

Perimeter of Parallelogram
The perimeter of any shape is the total distance covered around the shape or the total
length of any shape. Similarly, the perimeter of a parallelogram is the total distance of
the boundaries of the parallelogram. To calculate the perimeter value, we have to know
the values of its length and breadth. The parallelogram has its opposite sides equal in
length. Therefore, the formula to calculate the perimeter is written as;

Perimeter = 2 (a+b) units

Where a and b are the length of the sides of the parallelogram.

Types of Parallelogram
There are mainly four types of Parallelogram, depending on various factors. The factors
which distinguish between all of these different types of parallelogram are angles, sides
etc.
 1. In a parallelogram, say PQRS 

 If PQ = QR = RS = SP are the equal sides, then it’s a rhombus. All the

properties are the same for rhombus as for parallelogram.

2. Other two special types of a parallelogram are:

 Rectangle
 Square
A parallelogram is a two-dimensional geometrical shape, whose sides are parallel to
each other. It is a type of polygon having four sides (also called quadrilateral), where the
pair of parallel sides are equal in length. The Sum of adjacent angles of a
parallelogram is equal to 180 degrees. In geometry, you must have learned about many
2D shapes and sizes such as circle, square, rectangle, rhombus, etc. All of these shapes
have a different set of properties. Also, the area and perimeter formulas of these shapes
vary from each other and are used to solve many problems. Let us learn here the
definition, formulas and properties of a parallelogram.

Table of contents:

 Definition
 Shape
 Special cases
 Angle
 Properties
 Formula
 Types
 Theorems
 Parallelogram and Rhombus
 Examples
 Video Lesson
 FAQs

Parallelogram Definition
A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a
parallelogram are equal in length, and the opposite angles are equal in measure. Also,
the interior angles on the same side of the transversal are supplementary. Sum of all the
interior angles equals 360 degrees.
A three-dimensional shape that has its faces in parallelogram shape, is called a
parallelepiped. The area of parallelogram depends on the base (one of its parallel sides)
and height (altitude drawn from top to bottom) of it. The perimeter of a parallelogram
depends on the length of its four sides.
A square and a rectangle are two shapes which have similar properties of a
parallelogram.
Rhombus: If all the sides of a parallelogram are congruent or equal to each other, then it
is a rhombus.
If there is one parallel side and the other two sides are non-parallel, then it is a
trapezium.
See the figure below:
In the figure above, you can see, ABCD is a parallelogram, where AB || CD and AD ||
BC. 
Also, AB = CD and AD = BC
And, ∠A = ∠C & ∠B = ∠D
Also, ∠A & ∠D are supplementary angles because these interior angles lie on the same
side of the transversal. In the same way, ∠B & ∠C are supplementary angles.
Therefore,
∠A + ∠D = 180
∠B + ∠C = 180

Facts:

 Number of sides = 4
 Number of vertices = 4
 Mutually Parallel sides = 2 (in pair)
 Area = Base x Height
 Perimeter = 2 (Sum of adjacent sides length)
 Type of polygon = Quadrilateral

Shape of Parellelogram
A parallelogram is a two-dimensional shape. It has four sides, in which two pairs of sides
are parallel. Also, the parallel sides are equal in length. If the length of the parallel sides
is not equal in measurement, then the shape is not a parallelogram. Similarly, the
opposite interior angles of parallelogram should always be equal. Otherwise, it is not a
parallelogram.

Special Parallelograms
Square and Rectangle: A square and a rectangle are two shapes which have similar
properties of a parallelogram. Both have their opposite sides equal and parallel to each
other. Diagonals of both shapes bisect each other. 
Rhombus: If all the sides of a parallelogram are congruent or equal to each other, then it
is a rhombus.
Rhomboid: A special case of a parallelogram that has its opposite sides parallel to each
other but adjacent sides are of unequal lengths. Also, the angles are equal to 90
degrees.
Trapezium: If there is one parallel side and the other two sides are non-parallel, then it is
a trapezium. 

Angles of Parallelogram
A parallelogram is a flat 2d shape which has four angles. The opposite interior angles are
equal. The angles on the same side of the transversal are supplementary, that means
they add up to 180 degrees. Hence, the sum of the interior angles of a parallelogram is
360 degrees.

Properties of Parallelogram
If a quadrilateral has a pair of parallel opposite sides, then it’s a special polygon called
Parallelogram. The properties of a parallelogram are as follows:

 The opposite sides are parallel and congruent

 The opposite angles are congruent
 The consecutive angles are supplementary
 If any one of the angles is a right angle, then all the other angles will be at right
angle
 The two diagonals bisect each other
 Each diagonal bisects the parallelogram into two congruent triangles
 The Sum of square of all the sides of parallelogram is equal to the sum of square
of its diagonals. It is also called parallelogram law
Also, read:

 Parallelogram Law
 Diagonal of a Parallelogram Formula
 Important Questions Class 9 Maths Chapter 9 Areas Parallelograms

Formulas (Area & Perimeter)

The formula for the area and perimeter of a parallelogram is covered here in this section.
Students can use these formulas and solve problems based on them.

Area of Parallelogram
Area of a parallelogram is the region occupied by it in a two-dimensional plane. Below is
the formula to find the parallelogram area:
Area = Base × Height

In the above figure, ||gramABCD,  Area is given by;

Area = a b sin A = b a sin B

where a is the slant length of the side of ||gramABCD and b is the base.
Check here: Area of a Parallelogram Formula

Perimeter of Parallelogram
The perimeter of any shape is the total distance covered around the shape or the total
length of any shape. Similarly, the perimeter of a parallelogram is the total distance of
the boundaries of the parallelogram. To calculate the perimeter value, we have to know
the values of its length and breadth. The parallelogram has its opposite sides equal in
length. Therefore, the formula to calculate the perimeter is written as;

Perimeter = 2 (a+b) units

Where a and b are the length of the sides of the parallelogram.

Types of Parallelogram
There are mainly four types of Parallelogram, depending on various factors. The factors
which distinguish between all of these different types of parallelogram are angles, sides
etc.
1. In a parallelogram, say PQRS 

 If PQ = QR = RS = SP are the equal sides, then it’s a rhombus. All the

properties are the same for rhombus as for parallelogram.

2. Other two special types of a parallelogram are:

 Rectangle
 Square