 # Area and Perimeter

Area and Perimeter is an important topic in Mathematics, which is used in everyday life. This is applicable for any shape and size whether it is regular or irregular. You must have learned about different shapes such as triangle, square, rectangle, circle, sphere, etc. So the area is basically the space covered by these shapes and 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 cost for the same.

For Example, to fence the garden at your house, the length required of the material for fencing is the perimeter of the garden. If it’s a square garden with each side as a cm then 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 no. of tiles required to cover the whole floor. The formula for area and perimeter of some basic shapes are discussed here below.

## Definition of Area and Perimeter

Area: Area is the region bounded by the shape of an object. The space covered by the figure or any geometric shapes is the area of the shape. The area of all the shapes depends upon its dimensions and properties. Different shapes have different areas. The area of the square is different from the area of rhombus.

If two objects have a similar shape then its not necessary that area covered by them will be equal unless and until the dimensions of both the shapes are also equal. Suppose, there is two rectangle box, who has the length as L1 and L2 and breadth as B1 and B2. So the areas of both the rectangular box say, A1 and A2 will be equal only if L1=L2 and B1=B2.

Perimeter: Perimeter of a shape is defined as the total distance around the shape. Basically, its the length of any shape if it is expanded in a linear form. 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.

## 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.

### Area and Perimeter 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.

### Area and Perimeter 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.  And 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

Area of a circle is the region occupied by it in a plane. In 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 Chart

Here is the list of all 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(b + h) b=base h=vertical height

### Area and Perimeter Examples

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

Example 1: If the radius of a circle is 21cm. Find its area and circumference.

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, length of the side, a = 11 cm

Area = a= 11= 121 sq.cm

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

Example 3: The length of rectangular field is 12m and width is 10m. Find the area of the field along with its perimeter.

Solution: Given, Length = 12m

Width = 10m

Therefore, Area = length x width = 12 x 10 = 120 sq.m.

Perimeter = 2 (length + width) = 2 x (12 + 10) = 2 x 22 = 44 m.

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