Area and Perimeter of Shapes | Formula and Examples

Area and Perimeter mostly relate to 2-dimensional shapes. By learning about the areas of 2D shapes, we can easily determine the surface areas of 3D bodies and perimeter helps us to know the length required to cover the boundary of any 2D closed shape.

In this article, we are going to learn how to find the Area and Perimeter of different shapes, with the help of solved examples.

What is Area

Area is a measure of a region’s size on a surface.

In simple words, area helps us to know that how much space is occupied by a closed surface in a plane. Area is defined only for closed shapes. For a 2D geometric entity, area depends upon the shape and dimensions of the entity.

What is Perimeter

Perimeter is the length of a closed path that outlines a two dimensional shape.

For curved 2D shapes such as circle and ellipse, the perimeter is called as their circumference. By calculating perimeter of a region, one can determine the length required to surround that region on its boundaries.

Area and Perimeter Formulas

The table below provides a list of formulae to find values of area and perimeter of various 2D shapes.

Area and Perimeter Formulas for all Shapes
Shape	Area	Perimeter	Variables description
Triangle	A = 1/2(b × h)	P = a + b + c	b = base, h = height a,b and c are sides of triangle
Rectangle	A = l × b	P = 2(l+b)	l = length, b = breadth
Square	A = s × s	P = 4 × s	s = side
Circle	A = πr2	P = 2πr	r = radius, π = 22/7 or 3.14
Ellipse	A = π×b	P = π(a+b)	a = semi major axis b = semi minor axis
Parellelogram	A = b × h	P = 2(a+b)	b = base, h = height a and b are the opposite sides
Rhombus	A = 1/2 (d1 × d2)	P = 4 × a	d1, d2 = diagonals a = side of rhombus
Trapezium	A = 1/2 × (a+b) × h	P = Sum of all Sides	a,b = length of parallel sides, h = height

For polygons, perimeter can be calculated as sum of lengths of its sides. And, for a regular polygon, i.e a polygon having equal sides, perimeter is calculated as n × a, where n is number of sides or edges of the polygon and a is the measure of its one side.

Area and Perimeter of All Shapes

The 2D shapes have some specific properties related to their dimensions and orientation of their dimensions which they adhere to. They have defined formulae to calculate their area and perimeter.

Let’s discuss the formulae to calculate area and perimeter for various shapes.

Area and Perimeter of Triangle

A triangle is closed figure having three sides. It has three vertices. Altitude or height of a triangle is the perpendicular drawn from one of its vertex to meet the opposite side.

The side to which the perpendicular meets is called as the base of a triangle.

Area and Perimeter Formula of Triangle :

Area of a triangle = 1/2 × (base) × (height)

Perimeter of a triangle = Sum of all three sides

Area and Perimeter of Rectangle

A rectangle is a four sided polygon having opposite sides equal and parallel. All the angles of a rectangle are equal to 90°.

The longer side of a rectangle is known as the length of rectangle and the other side is called the breadth or width of rectangle.

Area and Perimeter Formula of Rectangle :

Area of a rectangle = length × breadth

Perimeter of a rectangle = 2 × (length + breadth)

Area and Perimeter of Square

A square is a four sided polygon having all four sides equal and parallel to each other. Also, all angles of a square have a measure of 90° each. Thus, a square can be said to be a special type of rectangle having all four sides equal.

Area and Perimeter Formula of Square:

Area of a Square = (side) × (side)

Perimeter of a Square = 4 × (side)

Area and Perimeter of Parallelogram

A parallelogram is a four sided polygon having opposite sides equal and parallel. The perpendicular distance between two opposite sides is called as the height of a parallelogram. The length of those sides is called as the base of a parallelogram.

Area and Perimeter Formula of Parellelogram :

Area of a Parellelogram = Base × Height

Perimeter of a Parellelogram = 2 × (Sum of opposite sides)

Area and Perimeter of Rhombus

A rhombus is a four sided polygon having all four sides equal and opposite sides being parallel to each other. The area of a rhombus is calculated by the measure of length of its diagonals.

Area and Perimeter Formula of Rhombus :

Area of a Rhombus = 1/2 × ( Product of diagonals)

Perimeter of a Rhombus = 4 × side

Area and Perimeter of Trapezium

Trapezium is a four sided polygon having two opposite sides parallel to each other. The other two sides may or may not be parallel. The distance between two parallel sides is known as the height of the trapezium.

Area and Perimeter Formula of Trapezium :

Area of a trapezium = 1/2 × (Sum of parallel sides) × (height)

Perimeter of a trapezium = (Sum of all 4 sides)

Area and Perimeter of Circle

A circle is a round shaped figure in which distance of all points lying on it from its center is equal . This distance is callled the radius of the circle. The perimeter of a circle is known as its circumference.

Area and Perimeter Formula of Circle :

Area of a Circle = πr²

Perimeter of a Circle = 2πr

Area and Perimeter of Semicircle

A semicircle is half of the circle whose one side is curved and other side is bounded by the diameter of the circle.

Area and Perimeter Formula of semicircle :

Area of Semicircle = 1/2 × π × r2

Perimeter of Semicircle = πr + 2r

Read More :

• Formulas of Semicircle

Difference between Area and Perimeter

The differences between Area and Perimeter are listed in form of a table below:

Area vs Perimeter
Area	Perimeter
Area is a measure of a region’s size on a surface. The region is a closed 2D figure.	Perimeter is a measure of the length of boundary of any closed 2D shape.
Area is expressed in square units, such as m2, cm2, mm2, etc.	It is expressed in units, such as m, cm, mm, etc.
Example: The space occupied by a park.	Example: The length of boundary of park.

Solved Examples on Area and Perimeter

Let’s solve some exsmple probkems on the Area and Perimeter formulas of different shapes.

Example 1: Find the values of perimeter and area for rectangular park having length as 40 m and the breadth as 50 m.

Solution:

Given,

Length of rectangle, l = 40 m

Breadth of rectangle, b = 50 m

We know that,

Perimeter of rectangle = 2(l+b) = 2×(40+50) = 2 × 90 = 180 m.

Area of rectangle = l × b = 40 × 0 = 2000 m²

Thus,

Perimeter = 180 m. and Area = 2000 m²

Example 2: A circular running track has a radius of 7 meters. Find its circumference. Take π = 22/7.

Solution:

We have,

Radius, r = 7 m and Circumference of a Circle = 2πr

Therefore,

Circumference = 2 × (22/7) × 7 = 44 meters

Thus, circumference of the circular track comes out to be 44 meters.

Example 3: The opposite sides of a parallelogram have values as 12 units and 8 units. Find the value of its perimeter.

Solution:

We know that,

Perimeter of parellelogram = 2 × (Sum of opposite sides)

Thus,

Perimeter = 2 × (12+8) = 2 × 20 = 40 units

Practice Questions on Area and Perimeter

Following are some practice questions based on calculating area and perimeter for you to solve.

Q1. Find the area of a trapezium whose parallel sides measure 12 cm and 14 cm. The distance between parallel sides is equal to 6 cm.

Q2. Calculate the perimeter of a regular pentagon having each side equal to 5 inches.

Q3. A circle has a diameter of 14 cm. Find the values of its circumference and area. Use, = 22/7.

Q4. The perimeter of a circle is 44 m. Find its radius and then calculate its area.

FAQs on Area and Perimeter

Define Area and Perimeter.

Area is defined as the space occupied by a geometrical shape.

Perimeter is defined as the length of boundary of a geometrical shape

What is the Difference between Area and Perimeter?

The difference between area and perimeter is that Area defines the region occupied by a 2D shape on a surface while Perimeter defines the length of the boundary on a 2D shape.

How to Find Area and Perimeter of Different Shapes?

To find area we need to multiply the dimensions of an object and To find the perimeter we need to take sum of the boundary of the object.

How to Find Area and Perimeter of Rectangle?

We can find the area of rectangle by finding the product of its length and breadth i.e. l × b and to calculate the perimeter we need to find the sum of its length and breadth and then multiply the sum by 2 i.e. Perimeter = 2(l + b)

What is Area and Perimeter of Circle Formula?

Area and Perimeter of a circle depends upon measure of its radius. Perimeter of a circle is generally called its circumference. Following are the formulae to calculate area and perimeter of a circle,

Area of a Circle = π×r²

Perimeter of a Circle = 2×π×r

where, π = pi whose value is taken as 22/7 or 3.14 commonly.

What is Area and Perimeter Formula of Square?

Area of a square: A=a² (where a is the length of a side)

Perimeter of a square: P=4a (where a is the length of a side)

What is Area and Perimeter of Rhombus Formula?

Area of a rhombus: A=( d₁ ​× d₂​​)/2 (where d₁ and d₂​​ are the lengths of the diagonals)

Perimeter of a rhombus: P=4a (where a is the length of a side)

What is Area and Perimeter of Trapezium Formula?

Area of a trapezium: A= 1/2​(a+b)h (where a and b are the lengths of the parallel sides and h is the height)

Perimeter of a trapezium: P=a+b+c+d (where a, b, c, and d are the lengths of the four sides)

How To Calculate Perimeter for a Polygon having n Sides?

A polygon is closed 2D shape having three or more sides. When all sides of the polygon are equal in length, it is called a regular polygon. For a regular polygon, perimeter is calculated as,

P = n × a

where, n is the number of sides of the polygon and a is the measure of each of its sides.

For a polygon, whose sides may be of different length, perimeter can be calculated as,

P = Sum of all sides

How To Calculate Area of Irregular Shapes?

For a irregular shape, we try to breakdown the shape into regular shapes such as triangle, rectangle or circle, and then, calculate the areas for each of the shape individually and sum up the individual areas to get the total area of the given irregular shape.

Is there any Direct Rrelation between Area and Perimeter of 2D Shapes?

Area and Perimeter do not have any direct mathematical relationship. Both area and perimeter measure different aspects related to any 2D figure, i.e. Area is the region covered by the figure on a surface and Perimeter is the length of boundary required to outline the shape.