Area and Perimeter - Difference between Area and Perimeter

Area and perimeter are two important topics in mathematics that help us understand the size and shape of objects. These concepts are used when we study two-dimensional shapes like triangles, rectangles, squares, and circles. 

Perimeter tells us the total length around the edge of a shape, while area tells us how much space is inside the shape. Every shape has its own formulas for area and perimeter, and knowing how to use them is very useful in solving problems. Here, we will learn the difference between area and perimeter in detail with their formulas and real-life examples.

Read More: Basic Geometrical Ideas

What is Area?

Area is the amount of space a shape covers on a flat surface. When we define an area, we are talking about the surface inside the boundaries of a shape. 

For example, if you spread a carpet on the floor, the region it covers is its area. If you want to paint a wall, you need to calculate the area of the wall. This will help you know how much paint is needed to cover it properly.

The same applies when you want to tile a floor, lay grass in a lawn, or place a sticker on your notebook. In all of these situations, you are calculating the area, which tells you how much surface is occupied.

We always use square units to calculate area because they represent how much space is covered within a shape. Common square units include:

•  Square centimeters (cm²), 

• Square meters (m²), and 

• square feet (ft²). 

For smaller surfaces like book covers or phone screens, we use cm². For larger surfaces like walls or rooms, we use m². The word “square” in the unit name reminds us that we are measuring how many little squares can fit into the shape.

To understand this better, imagine placing square tiles on a floor. The number of tiles that fit without overlapping gives you the area. For example, if a shape covers nine square tiles, its area is nine square units. No matter what shape you are working with, the area tells you how much space is filled or covered.

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What is Perimeter?

Perimeter is the total distance around the outside of a shape. It tells us how long the border of the shape is. You can think of it like a path that goes all the way around the edge. 

For example, if you want to put a fence around a garden, the length of the fence you need is the perimeter. If you walk all the way around a playground, the distance you walk is the perimeter of that playground.

To find the perimeter, you just add up the lengths of all the sides of the shape. For a rectangle, you add the two lengths and the two widths. For a square, since all four sides are the same, you just multiply one side by four. 

Perimeters are measured in units like:

• Centimeters, 

• Meters, 

• Feet, or 

• Inches.

Read More: What is Factor?

Difference Between Area and Perimeter

Let’s now understand the difference between area and perimeter with a simple comparison table:

Area and Perimeter Formulas

The table below shows the formulas for finding the area and perimeter of different shapes. These formulas will help students solve problems quickly and correctly when working with squares, rectangles, triangles, and circles.

 Read More: Types of Line in Math

Area and Perimeter Solved Examples

1. A square has side length 12 cm. Find its area and perimeter.

Solution:

We are given:

Side of square = 12 cm

Formula for Area of a square = side × side

Area = 12 × 12 = 144 square cm

Formula for Perimeter of a square = 4 × side

Perimeter = 4 × 12 = 48 cm

2. A rectangle has a length of 18 m and a width of 10 m. Find its area and perimeter.

Solution: 

We are given:
Length = 18 m

Width = 10 m

Formula for Area of a rectangle = length × width

Area = 18 × 10 = 180 square meters

Formula for Perimeter of a rectangle = 2 × (length + width)

Perimeter = 2 × (18 + 10) = 2 × 28 = 56 meters

3:  A triangle has a base of 16 cm and a height of 9 cm. Find its area.  Also, if the other two sides are 13 cm and 15 cm, find the perimeter.

Solution:
We are given:

Base = 16 cm

 Height = 9 cm

Other two sides = 13 cm and 15 cm

Formula for Area of a triangle = ½ × base × height

Area = ½ × 16 × 9 = 72 square cm

Formula for Perimeter of a triangle = sum of all sides

Perimeter = 16 + 13 + 15 = 44 cm

Example 4: If the radius of a circle is 21 cm, find its area and circumference. Use π = 22/7.

Solution:
We are given:

Radius = 21 cm

Formula for Area of a circle = π × r²

Area = 22/7 × 21 × 21 = 1386 square cm

Formula for Circumference of a circle = 2 × π × r

Circumference = 2 × 22/7 × 21 = 132 cm

5. A parallelogram has a base of 14 cm and a height of 8 cm. The opposite sides of the parallelogram are 14 cm and the other is 10 cm. Find its area and perimeter.

Solution:
We are given:

 Base = 14 cm

Height = 8 cm

The other side = 10 cm

Formula for Area of a parallelogram = base × height

Area = 14 × 8 = 112 cm²

Formula for Perimeter of a parallelogram = 2 × (base + side)

Perimeter = 2 × (14 + 10) = 2 × 24 = 48 cm.

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