Area and Perimeter Formula

Maths Area and Perimeter Formulas

As we know that geometry is the study of shapes. Geometry deals with plane shapes and solid shapes. We calculate different terms associated with the shapes, like length, width, height, area, perimeter, volume, etc. Area and volume are the two important concepts used in our daily life. We come across many shapes whose required space and distance around it have to be calculated and this is termed as the area and perimeter of the shapes. We see many shapes around like squares, rectangles, circles, polygon, etc. Every shape has its unique properties and measurements. Hence every shape has a different area and perimeter, based on their measurements. So here on this page, we will study Maths area and perimeter formulas associated with different shapes.


Area and Perimeter Definition

The area is the space occupied by any geometric figure and the perimeter is the distance around the shape or you can say boundary of the shape. 


Area

The area is the measurement of the space occupied by any two-dimensional geometric shapes. The area of any shape depends upon its dimensions. Different shapes have different areas. For instance, the area of the square differs from the area of the rectangle. The area of a shape is calculated in square units (sq units). 


Suppose if you want to paint the rectangular wall of your house, you need to know the area of the wall to calculate the quantity of the paint required to paint the wall and the cost of painting.


If two figures have the similar shape it is not necessary that they have equal area unless and until their dimensions are equal. Suppose two squares have sides s and s1, so the areas of the two square will be equal is s = s₁


Perimeter

A perimeter is the length of the boundary enclosed by any geometric shape. The perimeter of the shape depends on the length of the shape. For example, a metal wire of length 10cm can form both the circle and the square. 

Suppose you have to fence your house, the length required for fencing is the perimeter of the house.


Perimeters of two shapes can be equal only if their length is equal.


Area and Perimeter Formulas For all Shapes

There are different types of shapes with different dimensions.  So their area and perimeter formulas also differ. Here are the different area and perimeter formulas for all shapes. Given below is the area and perimeter formula chart which will provide you with the area and perimeter formulas for all shapes.


Area and Perimeter Formula Chart 

Name of Geometric shapes

Figure

Area Formula

Perimeter Formula

Variables

Rectangle

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Area = l × w

Perimeter = 2(l +w)

l =  length

w  = width

Square

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Area  = a2

Perimeter = 4a

a = sides of the square

Triangle

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Area = ½xbxh

Perimeter = sum of all sides

b = base

h = height

Trapezoid

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Area = 1/2(a + b)h

Perimeter = Sum of all sides.

a =base 1

b = base 2

h = vertical height

Parallelogram

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Area = b×h

Perimeter = 2(a + b)

a = side

b=base

h=vertical height


Rhombus

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Area = a x h

Perimeter = 4a

a = side of rhombus

h = height

Circle

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Area = πr2

Perimeter/Circumference  = 2r

r = radius of the circle

= 22/7 or 3.1416

Semicircle

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Area = ½ πr2


Perimeter = r + 2r

r = radius of the circle


This area and perimeter formula chart will help you to memorize these formulas at a glance. Keep this area and formula chart handy with you always.


Solved Examples

Here are some solved examples based on the area and perimeter formulas of different shapes.

Example 1:

If the radius of a circle is given as 7cm. Find its area and circumference.

Solution:

Given that radius = 7cm

We have, Area A = π × r2

A = 22/7 × 7 × 7

A = 154cm2.

And Circumference, C = 2πr 

C = 2 x 22/7 x 7

C  = 44 cm


Example 2:

If the length of the side of a square is 9cm. Then find its area and the total length of its boundary.

Solution:

Given that length of the side of square, a = 9 cm

We have Area formula as A = a2

 = (9)2 

= 81 cm2

Total length of its boundary is the Perimeter of the square 

We have perimeter = 4a 

= 4 x 9 

= 36cm.

Therefore area of square is 81cm2 and total length of its boundary is 36cm


Example 3:

The length of the rectangular field is 15m and width is 6m. Find the area and perimeter of the field 

Solution:

Given that   Length = 15m

Width = 6m


We have,  Area formula A = length x width 

    = 15 x 6 

    = 90 m2

 And Perimeter formula P = 2 (length + width) 

   = 2 x (15 + 6) 

   = 2 x 21

   = 42 m.


Quiz Time

Check your progress by solving some more problems in the area and perimeter of different shapes.

  1. Find the cost of carpeting a room 13m long and 9m broad at the rate of 12.40 rs per meter.

  2. The area of a square is 121sq.cm. Find its side.

FAQ (Frequently Asked Questions)

1. What is the Difference Between Area and Perimeter?

Answer: Area is defined as the space occupied by the shape. While perimeter id defined as the distance around the shape(the boundary of the shape).


Shapes with the same area can have different perimeters and the shapes with the same perimeter can have different areas. The area is measured in square units and the perimeter is measured in linear units. The area can be measured for 2 - dimensional objects while the perimeter is measured for one-dimensional shapes.

The below figure represents the difference between area and perimeter.

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2. What is the Difference Between Area and Volume?

Answer: Area refers to the space occupied by the object. And volume refers to the quantity or capacity of the object. An area is a two-dimensional object whereas volume is a three-dimensional object. The area is a plain figure while volume is a solid figure. The area covers the outer space and volume covers the inner capacity. The area is measured in square units and volume is measured in cubic units. Here is the pictorial representation of area and volume.

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