Relationship Between Area and Perimeter
As we know, geometry is the study of shapes. Geometry deals with plane shapes (two-dimensional) and solid shapes (three-dimensional). We calculate different terms associated with the shapes, like length, width, height, area, perimeter, volume, etc. Area and Perimeter are the two important concepts used in our daily life and is important for JEE Main Exam.
So what is Area? What is the Perimeter? We come across many shapes whose required space and distance around them have to be calculated and this is termed as the area and perimeter of the shapes. Every shape has its unique properties and measurements. Hence, every shape has a different area and perimeter, based on its measurements. So here in this post, we will study the relationship between area and perimeter, and what is the difference between area and perimeter?
What is Area?
The area is the measurement of the space occupied by any two-dimensional geometric shape. The area of any shape depends upon its dimensions. Different shapes have different areas. For instance, the area of the square differs from the area of the rectangle. The area of a shape is calculated in square units (sq units).
Suppose if you want to paint the rectangular wall of your house, you need to know the area of the wall to calculate the quantity of paint required to paint the wall and the cost of painting.
If two figures have a similar shape it is not necessary that they have equal area unless and until their dimensions are equal. Suppose two squares have sides s and s1, so the areas of the two squares will be equal if s = s1
The formula for Area is a product of length and width.
What is a Perimeter?
A perimeter is the length of the boundary enclosed by any geometric shape. The perimeter of the shape depends on the length of the shape. For example, a metal wire of length 10cm can form both the circle and the square.
Suppose you have to fence your house, the length required for fencing is the perimeter of the house.
Perimeters of two shapes can be equal only if their length is equal.
The perimeter formula is the sum of all sides of a shape.
What is the Difference between Area and Perimeter?
As we have understood what is area and what is perimeter let us understand the relationship between area and perimeter.
The area is defined as the space occupied by the shape. The perimeter is defined as the distance around the shape(the boundary of the shape).
Shapes with the same area can have different perimeters and the shapes with the same perimeter can have different areas. The area is measured in square units and the perimeter is measured in linear units.
The area can be measured for 2 - dimensional objects while the perimeter is measured for one-dimensional shapes.
The below figure represents the difference between area and perimeter.
Area Vs Perimeter
Key Differences between Area and Perimeter are:
Perimeter and Area Formulas for All Shapes
Now let us study what is the difference between area and perimeter formulas.
There are different types of shapes with different dimensions. Hence, their perimeter and area formulas also differ. Here are the different area and perimeter formulas for all shapes. Given below is the perimeter vs area formula chart which will provide you with the perimeter and area formulas for all shapes.
Perimeter Vs Area Formula Chart
This area and perimeter formula chart will help you to memorize these formulas at a glance. Keep this perimeter vs area formula chart handy with you always.
Application of Area in Real Life
In the practical world, shapes can be complex in nature. Suppose you want to order a carpet for the floor in your home. For this, you should know the area of the floor to order the right quantity and size of the carpet. A typical floor plan of a room may not necessarily be a triangle or a square.
In such a scenario, the trick is to split the shape into several rectangles or squares. It doesn’t matter how you split the shape.
Also, when building a rectangular jogging park with a garden in the center, the concept of an area can be applied. The area of the jogging track can be calculated by subtracting the area of the garden present in the center from the area of the whole rectangular garden. In this way, one can precisely know the area of the jogging track before starting any construction activities.
Application of Area of the Triangle in Real Life
1. Traffic Signs
The triangles used in traffic signs are equilateral triangles. The traffic rules are stated in a diagrammatic form in such triangles, where it becomes easy to spot and read them.
2. Truss Bridges
Truss bridges are supporting structures constructed in triangular shapes. The reason behind using triangles in constructing such support structures is that they evenly distribute the weight without changing the proportions. This way the bridges built are very strong and can hold much more weight. One can see truss bridges when a train passes over a river.
3. Sailing Boat
The small sailboats present in the seas often have a triangular sail. By using a triangular sail design, it has become easier to travel against the wind in the open seas. The technique used here is called tacking. Tacking allows the boat to move forward with the wind at right angles to the boat.
Application of Perimeter in Real Life
1. Planning the construction of a house. Since concrete has to be poured in for a solid foundation, knowing the perimeter precisely is imperative to pour concrete in the right quantities within the housing boundary constraints.
2. In shapes like a cone, cylinder, sphere, etc. knowing the perimeter and area helps to know the volume of the shape. This way one can know the quantity of liquid that can be accommodated in it.
3. Knowing the perimeter of the houses helps to predict precisely the amount of paint that would be required to paint the outside walls.
4. Before constructing colonies. Before building a large colony on a vast piece of land, knowing the perimeter helps to know the number of raw materials that would be required to build boundary fencing. Apart from that, splitting the large area into small units of rectangular or square shape and determining its area with perimeter makes it easy for architects to develop the various building plans before commencing construction activities.
Solved Examples for Area and Perimeter
Here are some solved examples based on the area and perimeter formulas of different shapes.
Example 1: If the radius of a circle is given as 7cm. Find its area and circumference.
Solution:
Given that radius = 7cm
We have, Area A = π × r2
A = 22/7 × 7 × 7
A = 154cm2.
And Circumference, C = 2πr
C = 2 x 22/7 x 7
C = 44 cm
Example 2: If the length of the side of a square is 9cm. Then find its area and the total length of its boundary.
Solution:
Given that length of the side of square, a = 9 cm
We have Area formula as A = a2
= (9)2
= 81 cm2
Total length of its boundary is the Perimeter of the square
We have perimeter = 4a
= 4 x 9
= 36cm.
Therefore the area of the square is 81cm2 and total length of its boundary is 36cm
Example 3: The length of the rectangular field is 15m and the width is 6m. Find the area and perimeter of the field
Solution:
Given that Length = 15m
Width = 6m
We have, Area formula A = length x width
= 15 x 6
= 90 m2
And Perimeter formula P = 2 (length + width)
= 2 x (15 + 6)
= 2 x 21
= 42 m.
Example 4: The side length of a rhombus is 8 inches and the height of a rhombus is 12 inches. Find the area and perimeter of the given rhombus.
Solution:
Given that side length/ base/ a = 8 inches
Height h = 12 inches
We have, Area formula A = base x height
= 8 x 12
= 96 inches2
And Perimeter formula P = 4 (side length)
= 4 x (8)
= 32 inches.
Example 5: Find the area and perimeter of a trapezoid whose parallel sides are given as 45 cm and 36 cm and non-parallel sides are 30 cm and 52 cm respectively. Its height is 12 cm.
Solution:
Given that sides
a = 45 cm
b = 36 cm
And height h= 12 cm.
We have, Area formula A = 1/2 (a+b)h
= 1/2 (45+36)x12
= 1/2 x 81x12
= 972/2
= 486 cm2
Perimeter formula P = sum of all sides
= a+b+c+d
= 45+36+30+52
= 163 cm.
Quiz Time
Check your progress by solving some more problems in the area and perimeter of different shapes.
Find the cost of carpeting a room 13m long and 9m broad at the rate of 12.40 rs per meter.
The area of a square is 121sq.cm. Find its side.
Conclusion
Understanding the difference between area and perimeter through Perimeter And Area Definition and Area And Perimeter Examples on our page, is essential in geometry. While the area measures the surface enclosed by a shape, the perimeter represents the total length of its boundary. These concepts are used in various real-world applications, from calculating floor space to fencing a property. By knowing when to use area or perimeter, you can solve problems more effectively and apply these measurements in practical scenarios.
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FAQs on Difference Between Area And Perimeter - JEE Main 2025
1. What is the Difference Between Area and Volume?
Area refers to the space occupied by the object. And volume refers to the quantity or capacity of the object. An area is a two-dimensional object whereas volume is a three-dimensional object.
The area is a plain figure while volume is a solid figure. The area covers the outer space and volume covers the inner capacity. The area is measured in square units and volume is measured in cubic units. Here is the pictorial representation of area and volume.
2. What is Heron’s Formula in the context of the area?
There are 3 types of triangles, namely, the Isosceles triangle, the Equilateral triangle and the Scalene triangle. A scalene triangle is a type of triangle that has all three sides of different lengths. When it comes to calculating the area of a Scalene triangle, heron’s formula is used. Scalene triangle area is calculated as
Scalene triangle area = $\sqrt{s(s-a)(s-b)(s-c)}, where $s=\frac{(a+b+c)}{2}$.
Here a, b and c are sides of the triangle.
3. Explain briefly what you mean by perimeter? How can you calculate the perimeter of a triangle?
In simple words, the perimeter is the total length of the exterior boundaries of any given shape. It is measured in linear units since it represents one-dimensional objects and is primarily concerned with the length of the shape. The perimeter of a triangle can be calculated by adding all three sides of a triangle. The formula for the perimeter of a triangle is given as
Perimeter of triangle = a + b + c
Where a,b,c represent the length of the three sides of the triangle.
4. Explain where the concept of area and triangle be applied in practical life?
Before the construction of any building, the architect needs to figure out the area of the built-up area of the land on which the building is to be constructed, creating an efficient plan to build the carpet area of rooms, perimeter to build different walls and build its fencing, area of the footpath that will surround the ground, etc. Also, when designing the plan of children’s parks or gardens, architects take into account the knowledge of area and perimeter to design an efficient plan to build the park for maximum use.
5. What is the difference between Area and Perimeter? Give Perimeter And Area Definition.
Area refers to the amount of space inside a 2-dimensional shape, measured in square units (like square meters). It tells you how much space a shape covers.
Perimeter is the distance around the outside of a 2-dimensional shape. It's the total length of all sides combined.
6. Can you give Area And Perimeter Examples?
Example of Area: The area of a rectangle with length 5 meters and width 3 meters is 15 square meters (5 × 3 = 15).
Example of Perimeter: The perimeter of a square with each side 4 meters long is 16 meters (4 + 4 + 4 + 4 = 16).
7. How to find Area and Perimeter of different shapes?
Rectangle: To find the area, multiply length by width; to find the perimeter, add all four sides.
Circle: Area is πr² (pi times radius squared); perimeter is 2πr (twice pi times radius).
Triangle: Area can be calculated using base and height; perimeter is the sum of all three sides.
8. Why are Area and Perimeter important?
Area helps in determining how much space is enclosed or occupied by a shape, which is crucial in construction, landscaping, and other fields.
Perimeter is vital for measuring boundaries, such as fencing, or determining the amount of material needed for the edges of objects.
9. Are perimeter and area equal?
The key difference between area and perimeter is: area is the region occupied by shape and perimeter defines the length of the outer boundary of the shape.
10. What is the relation of perimeter to area?
Area and perimeter are directly related only for circles. Given only the area or only the perimeter of any other shape does not inform the other quantity.
