Difference Between Area and Perimeter
Area and Perimeter are two important concepts. Sometimes, the term 'Area' is confused with 'Perimeter'. They both are entirely different. The area is defined as the amount of space occupied by any two-dimensional shape. Perimeter defines the boundary or outline of a flat shape. The methods of measuring area and perimeter are completely different. Let us discuss the key differences between these two important terms.
Definition of Area
Area is defined as the amount of space that is occupied by any shape, object, or flat surface. The total number of square units that can fit into a shape or an object or a flat surface defines the actual area. The concept of finding an area can easily be understood by using a square grid paper. The total number of unit square enclosed in the figure gives the area of that figure. For example, the blue square occupies 9 squares, which means the area of the square is 9 square units. In real life, we use the concept of area to find out the amount of space that is to be painted in a wall, the dimensions of a room, the space in the floor of a room that is to be covered by tiles, making a lawn at the backyard and so on.
Definition of Perimeter
The word 'perimeter' is derived from the Greek word 'Perimetron'. 'Peri' means 'around' and 'Metron' means 'measure'. The perimeter of a shape is calculated by adding up the length of all the sides or by measuring the outer boundary of a shape or an object. Some real-life uses of the perimeter are to know about the size of a photo frame, length of a lawn that for which we need to put a fence. Perimeters of small objects can be found by taking a string or a thread around the object for which perimeter is to be found. In the case of polygons, their perimeter can be found by adding up the sides of the polygon and expressing them in the given units. The figure given below shows the perimeter of a square, which is 20 units.
What is the Difference Between Area and Perimeter?
The following table lists the important differences between area and perimeter.
|Area refers to the space occupied by a shape or an object or a surface.||Perimeter refers to the measure of the length of the outline or boundary of a shape, an object or a surface.|
|Area is measured in square units. For example, if the dimensions are in inches, then the area is expressed as square inches.||Perimeter is measured in linear units. For example, if the dimensions are in inches, then the perimeter is expressed as inches.|
|Example: Area of a square park is side of the park × side of the park or side2||Example: The perimeter of the square park is the sum of all the 4 sides of the park or 4 × side.|
Area and Perimeter Formula
The table given below lists some important formulas for the area and perimeter of some common shapes.
|Shape||Area (square units)||Perimeter (units)|
|Square||side × side||4 × side|
|Rectangle||length × width||2(length + width)|
|Equilateral Triangle||side + side + side||(1/2) × base × height|
|Parallelogram||2 × (sum of two parallel sides)||base × height|
|Rhombus||4 × side||(1/2) × diagonal 1 × diagonal 2|
Topics Related to Area and Perimeter
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Solved Examples on Area and Perimeter
Example 1: Find the area and perimeter of a square with a side length of 7 units.
Area of a Square = (side × side) square units. The side of the square = 7 units (given). Therefore, area of square = 7 × 7 = 49 square units. Perimeter of a Square = (4 × side) units. The side of the square = 7 units. Therefore, perimeter of the square = 4 × 7 = 28 units.
Example 2: The length of a rectangular carpet is 21 units. Its area is 210 square units. Find the width of the carpet and the perimeter of the carpet.
Area of a rectangle = (length × width) square units. Given, length of the rectangular carpet = 21 units and area = 210 square units ⇒ 21 × width = 210 ⇒ width = 210/21. Thus, the width of the rectangular carpet= 10 units.
Now, Perimeter of a rectangle = 2(length + width) units. Given: length of the rectangular carpet = 21 units and width of the rectangular carpet = 10 units. Substituting the values of length and width in the formula we get, perimeter = 2 (21 + 10) = 2 (31) = 62 units. Therefore, the perimeter of the rectangular carpet = 62 units.
Example 3: A circular-shaped garden has a radius of 50 units has to be fenced. Find the cost of fencing the circular garden if it takes $10 to fence one unit. (Use the value of π as 22/7)
To calculate the cost of fencing the garden, we first have to find the outer boundary length of the garden. To find that let us find the perimeter of the circular garden with a radius of 50 units. For a circle, the circumference = 2πr units.
Given: radius = 50 units. Therefore, circumference = 2 × (22/7) × 50 = 314.28 units. The cost of fencing 1 unit of the garden = $10. Therefore, the cost of fencing 314.28 units of the garden = 314.28 × 10 = $3142.8
FAQs on Difference Between Area and Perimeter
How Are Area and Perimeter Related?
Area is defined as the measure of space occupied by any surface or object, whereas perimeter defines the length of the boundary of an object or a shape.
What is the Unit of Measurement for Perimeter and Area?
Perimeter is measured in linear units and area is measured in square units. For example, if the length and width of a rectangle are 6 units and 4 units respectively, then its perimeter is 20 units and the area of the rectangle is 24 square units.
Is Circumference Area or Perimeter?
The perimeter of a circle is referred to as its circumference.
What is the Difference Between Perimeter and Circumference?
Perimeter is measured by calculating the length of the boundary of a surface or a shape. For a circle, the perimeter is referred to by the term 'Circumference'. The circumference of a circle is calculated by using the formula 2πr units.
How to Calculate the Area of a Square?
Area of a square is calculated using the formula (side × side) square units if the length of its side is given. For example, the area of a square with side length 5 units is 5 × 5, which is equal to 25 square units.
What is the Difference Between Area and Perimeter?
Area is defined as space or the region occupied by a shape, whereas perimeter is defined as the boundary or the outline of a shape. Two shapes with the same areas can have a different value for the perimeter. The area is measured in square units, whereas the perimeter is measured in linear units.