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:
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.
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:
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Centimeters,
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Meters,
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Feet, or
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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:
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Difference Between Area and Perimeter
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Aspects
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Area
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Perimeter
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Meaning
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Area is the space inside a shape. It shows how much surface the shape covers.
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Perimeter is the total distance around a shape. It shows the length of the boundary.
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What it measures
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It measures surface or space
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It measures the length around the outside edge.
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Units Used
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Measured in square units, like cm², ft², m², or in²
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Measured in regular units, like cm, ft, m, or in.
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How to Calculate
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Use multiplication based on shape (for example, length × width).
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Use addition (add all the sides together).
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Example (Rectangle)
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Area = length × width.
For a 50 m × 30 m rectangular shape, the area will be 150 m².
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Perimeter = 2 × (length + width). For 50 m and 30 m, perimeter = 2 × (50 +30) = 80 m.
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Used For
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Finding how much space is needed to cover something.
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Finding how much material is needed to go around something.
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Real- Life Example
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Tiling a floor, painting a wall, laying carpet.
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Fencing a yard, putting a border around a picture, sewing edges of a cloth.
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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.
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Difference Between Area and Perimeter
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Shapes
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Area
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Perimeter
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Terms
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Circle
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Area = π × r²
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Circumference = 2πr
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R= Radius
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Triangle
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Area = ½ × Breadth × Height
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Side = a + b + c
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Here, the variable (a, b, and c) represents the side of a triangle
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Square
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A = a²
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P = 4a
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Here a represents the side of the square
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Rectangle
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A = Length × width
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P = 2(l + w)
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Here,
L = length
W = Width
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Parallelogram
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A = Breadth × Height
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P = 2(a + b)
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Here,
a is side and b is base
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Read More: Types of Line in Math
Area and Perimeter Solved Examples
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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
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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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