Area And Perimeter- Definition, Formula And Examples

Area and perimeter, in Math, are the two important properties of two-dimensional shapes. Perimeter defines the distance of the boundary of the shape whereas area explains the region occupied by it. Area and Perimeter is an important topic in Mathematics, which is used in everyday life. This applies to any shape and size whether it is regular or irregular. Every shape has its own area and perimeter formula. You must have learned about different shapes such as triangles, squares, rectangles, circles, spheres, etc. The area and perimeter of all shapes are explained here.  Join Safalta School Online and prepare for Board Exams under the guidance of our expert faculty. Our online school aims to help students prepare for Board Exams by ensuring that they have conceptual clarity in all the subjects and can score their maximum in the exams.
 

What is Area?

The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape. The area of all the shapes depends upon their dimensions and properties. Different shapes have different areas. The area of the square is different from the area of a kite.

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If two objects have a similar shape then the area covered by them doesn’t need to be equal unless and until the dimensions of both shapes are also equal. Suppose, there are two rectangle boxes, with length as L1 and L2 and breadth as B1 and B2. So the areas of both the rectangular boxes, say A1 and A2 will be equal only if L1=L2 and B1=B2.
 

What is Perimeter?

The perimeter of a shape is defined as the total distance around the shape. Perimeter is the length of any shape if it is expanded in a linear form. A perimeter is a total distance that encompasses a shape, in a 2d plane. The perimeter of different shapes can match in length with each other depending upon their dimensions.

For example, if a circle is made of a metal wire of length L, then the same wire we can use to construct a square, whose sides are equal in length.

 

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What is the Difference Between Area and Perimeter?

Here is the list of differences between area and perimeter:

Area	Perimeter
Area is the region occupied by a shape	Perimeter is the total distance covered by the boundary of a shape
Area is measured in square units (m2, cm2, in2, etc.)	Perimeter is measured in units (m, cm, in, feet, etc.)
Example: The area of rectangular ground is equal to the product of its length and breadth.	Example: The perimeter of a rectangular ground is equal to the sum of all its four boundaries, i.e., 2(length + breadth).

 

Area and Perimeter For all Shapes

There are many types of shapes. The most common ones are Square, Triangle, Rectangle, Circle, etc. To know the area and perimeter of all these, we need different formulas.

 

The perimeter and Area of a Rectangle

A rectangle is a figure/shape with opposite sides equal and all angles equal to 90 degrees. The area of the rectangle is the space covered by it in an XY plane.
 

Perimeter of a Rectangle = 2(a+b) Area of Rectangle = a × b

where a and b are the length and width of the rectangle.
 

Perimeter and Area of a Square

A Square is a figure/shape with all four sides equal and all angles equal to 90 degrees. The area of the square is the space occupied by the square in a 2D plane and its perimeter is the distance covered on the outer line.

Perimeter of a Square = 4a Area of a Square = a2

where a is the length of the side of the square.

 

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Perimeter and Area of Triangle

The triangle has three sides. Therefore, the perimeter of any given triangle, whether it is scalene, isosceles, or equilateral, will be equal to the sum of the length of all three sides.  The area of any triangle is the space occupied by it in a plane.

 

Perimeter of a triangle = a + b +c, where a, b, and c are the three different sides of the triangle. Area of a triangle = 1/2 b × h; where b is the base and h is the height of the triangle.

 

Area and Circumference of Circle

The area of a circle is the region occupied by it in a plane. 

 

In the case of a circle, the distance of the outer line of the circle is called the circumference.

Circumference of Circle = 2πr Area of Circle = πr2

 

Area and Perimeter Formulas

Here is the list of the area and perimeter for different figures in a tabular form. Students can use this table to solve problems based on the formulas given here.

Shape	Area	Perimeter	Terms
Circle	A = π × r2	Circumference = 2πr	r = radius of the circle
Triangle	A = ½ × b × h	S = a+b+c	b = base   h = height a,b and c are the sides of the triangle
Square	A = a2	P = 4a	a = length of side
Rectangle	A = l × w	P = 2(l + w)	l = length   w = width
Parallelogram	A = b × h	P = 2(a+b)	a = side   b=base h=vertical height

 

Applications of Area and Perimeter

We know that the area is the space covered by these shapes and the perimeter is the distance around the shape. If you want to paint the walls of your new home, you need to know the area to calculate the quantity of paint required and the cost for the same.

For example, to fence the garden in your house, the length required of the fencing material is the perimeter of the garden. If it’s a square garden with each side as a cm then the perimeter would be 4a cm. The area is the space contained in the shape or the given figure. It is calculated in square units. Suppose you want to fix tiles in your new home, You need to know the area of the floor to know the number of tiles required to cover the whole floor. In this article, let us have a look at the formula for the area and perimeter of some basic shapes with diagrams and examples.

 

Solved Examples of Area and Perimeter

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

Example 1:

If the radius of a circle is 21cm. Find its area and circumference.

Solution:

Given, radius = 21cm

Therefore, Area = π × r2

A = 22/7 × 21 × 21

A = 1386 sq. cm.

Circumference, C = 2πr 

C = 2 x 22/7 x 21 = 132 cm

Example 2:

If the length of the side of a square is 11cm. Then find its area and also find the total length of its boundary.

Solution:

Given, the length of the side, a = 11 cm

Area = a2 = 112 = 121 sq.cm

The total length of its boundary, Perimeter = 4a = 4 x 11 = 44 sq. cm.