Area and Perimeter

Area and perimeter are two key properties of any shape that help us determine various quantities and estimates. The shapes are all around us, from the circular pizza we eat to the rectangular plots we build on. Understanding how to calculate the area and perimeter of shapes helps us to make sense of the world around us. Whether it is painting walls, planning parties, or constructing houses, we use them almost every day. We need to know the area and perimeter of a shape for tasks such as laying down tiles, fencing a plot, wrapping a gift, painting a wall, or planting a garden. Construction, architecture, painting, designing, and planning are some of the primary domains where we use the area and perimeter of geometrical shapes to our advantage. Let’s learn more about the area and perimeter of various shapes and how to apply them in real life.

 

Table of Contents

• What Is Area of a shape?
• What Is Perimeter?
• What is the Difference Between Area and Perimeter?
• Units of Measurement
• Area and Perimeter Formula
• Area and Perimeter of Common Shapes
• Real-Life Examples of Area and Perimeter
• Word Problems Using Formula of Area and Perimeter
• Common Mistakes to Avoid
• Practice Questions
• Conclusion
• FAQs on Area and Perimeter

 

What Is Area of a shape?

The area of a shape is the space enclosed within its boundary. It tells us how much space is occupied by any shape and is usually calculated in square units like square centimeters or square meters. We can use formulas to measure the area of rectangular boxes, square playgrounds, circular pools, and so many other objects using the different formulas of area.

For example, to calculate the area of a rectangular plot, we use the formula Area = Length X Breadth.

As area refers to the surface covered within a shape or figure, it is measured in square units such as square centimetres (cm²), square meters (m²), etc. For instance, If a square tile is 1 meter long on each side, the area it covers is 1 square meter.

 

What Is Perimeter of a shape?

The perimeter of a shape is the total length of the boundary of a shape. In other words, it is the distance covered along the border of a closed shape. To calculate the perimeter of a shape, we have to add the length of each side. It is measured in linear units or units of length such as meters (m), centimetres (cm), inches, etc. The perimeter of a curved shape like a circle is called an ellipse. The formula to calculate the perimeter of a rectangle is: Perimeter = 2(Length + Breadth).

Example: If a rectangle has a length of 5 meters and a width of 2 meters, then the perimeter is the total distance around it measured as 2 (5 + 2) = 14 meters.

 

What is the Difference Between Area and Perimeter?

Area and perimeter are different in terms of what they measure. While area measures the space inside a shape, perimeter is the distance around the shape. We apply the formula of area to find the cost of flooring, painting, or land area, whereas perimeter formulas are used to calculate the fencing, edging or border length. Area is calculated in square units (cm2, m2, in2, etc) and perimeter is calculated in linear units (cm, m, in, etc). For curved 2-d shapes like circles and ellipses, the perimeter is called its circumference.

 

Units of Measurement

Depending on the size and object, different units are used:

 

Make sure the units for all sides are the same before applying any formula.

 

Area and Perimeter Formula

Shape	Area	Perimeter
Square	side × side	4 × side
Rectangle	length × width	2 (length + width)
Triangle	½ × base × height	Perimeter of triangle = sum of all sides
Circle	Area = π × radius²	2 × π × radius
Trapezium	½ × (sum of parallel sides) × height	Perimeter = the sum of all sides
Parallelogram	base × height	2 × (base + side)

These area and perimeter formulas are widely used in both academic and practical situations.

 

Area and Perimeter of Common Shapes

There are many different shapes like squares, circles, triangles, rectangles, etc and different formulas are used to calculate their area and perimeter. Here are some of the 2-d shapes along with the formulas to measure their area & perimeter:

1. Area and perimeter of a square: 

A square is a special type of rectangle with four equal sides and four right angles. From this definition of a rectangle, we can also say that every square is a rectangle because it has four sides meeting each other at right angles. However, not every rectangle is a square, since a rectangle’s length and width don’t have to be the same. 

The formulas to calculate the perimeter and area of a square:

• Area of a square = side × side

• Perimeter of a square = 4 × side

Example

To find the area of a square with side = 5 cm we can apply the above formulas as:

• Area = 5 × 5 = 25 cm²

• Perimeter = 4 × 5 = 20 cm
  
  

2. Area and perimeter of a rectangle: 

A Rectangle is one of the most common shapes around us. The word “rectangle” is derived from the Latin word rect (right) and the French word angle (angle). So, a rectangle is a shape that contains four sides intersecting each other at right angles. As the sides of a rectangle are always parallel, it makes the rectangle a type of parallelogram. The opposite sides of a rectangle are always of the same length. The formulas to calculate the perimeter and area of a rectangle:

• Area of rectangle = length × width

• Perimeter of rectangle = 2 × (length + width)

Example

To find the area & perimeter of a rectangle with Length = 8 m, Width = 3 m , we can apply the above formulas as:

• Area = 8 × 3 = 24 m²

• Perimeter = 2 × (8 + 3) = 22 m
  
  

3. Area and perimeter of a triangle: 

Triangular shapes have real-life applications as they are strong and reliable. Some common examples of triangles are roofs, pyramids in Egypt, truss bridges, etc. A triangle has three sides; therefore, the perimeter of a triangle is the sum of the lengths of its three sides.

The formulas to calculate the area & perimeter of a triangle:

• Area of triangle= ½ × base × height

• Perimeter of triangle = sum of all sides

Example

Area and perimeter of triangle with Base = 10 cm, Height = 5 cm and Sides = 10 cm, 7 cm, 6 cm

• Area = ½ × 10 × 5 = 25 cm²

• Perimeter = 10 + 7 + 6 = 23 cm
  
  

4. Area and perimeter of a circle: 

A Circle is a basic geometric shape widely used across our lives, from car wheels to coins and rings. The perimeter of a circle is called a circumference and is calculated using the formula 2π𝑟, where r represents the radius of a circle.

The formulas to calculate the area & circumference of a circle:

• Area = π × radius²

• Perimeter (Circumference) = 2 × π × radius

Example

Radius = 7 cm

• Area = π × 7² = 154 cm² (approx)

• Perimeter = 2 × π × 7 = 44 cm (approx)

These examples show how useful area of perimeter formula can be.

 

Real-Life Examples of Area and Perimeter

There are many applications of the area & perimeter of shapes. The foundation of a house is usually rectangular in shape; by finding the perimeter of the foundation, we can calculate the cost of raising a proper foundation for the house. By finding the area of a rectangular plot, we can estimate the floor area and cost of material used for construction. Gardening is another such example where area and perimeter will help us plant flowerpots all across the perimeter of a garden. Knowing the perimeter & area of a square lawn will help to plant flowerpots all across the perimeter of the lawn and understand the quantity of seeds required to cover the whole lawn. Some of the other important applications of area and perimeter is listed below:

• Fencing a Garden: You need to calculate the perimeter to buy the correct length of fence.

• Painting a Wall: Calculate the area to know how much paint to buy.

• Designing a Playground: Determine area to plan space for slides and swings.

• Buying Carpet: Know the area of the floor to purchase the right size.

These real-world uses show the value of understanding the formula of area and perimeter.

 

Word Problems Using Formula of Area and Perimeter

Q1. A rectangular floor is 10 m long and 8 m wide. Find the area and perimeter.

• Area = 10 × 8 = 80 m²

• Perimeter = 2 × (10 + 8) = 36 m
  
  

Q2. A square playground has a side of 20 m. How much fencing is needed?

• Perimeter = 4 × 20 = 80 m
  
  

Q3. A circular pond has a radius of 14 m. What is the area?

• Area = π × 14² = 615.75 m² (approx)

Word problems give practice applying the area and perimeter formula in real scenarios.

 

Common Mistakes to Avoid

• Mixing up area and perimeter (area is space inside, perimeter is the boundary)

• Using wrong units (always convert to the same unit before solving)

• Forgetting π ≈ 3.14 in circular calculations

• Forgetting to square the radius when calculating area of a circle

• Using height instead of side in square formulas

Careful reading and double-checking can prevent errors when solving math area and perimeter questions.

 

Practice Questions

1. Find the area and perimeter of a rectangle with length 15 cm and width 4 cm.

2. A square has a side of 12 m. What is its area and perimeter?

3. A triangle has a base of 10 cm and height of 6 cm. What is the area?

4. Find the perimeter of a triangle with sides 7 cm, 8 cm, and 9 cm.

5. A circle has a radius of 5 cm. Find its area and circumference.

Practice these to get more comfortable with the area and perimeter formula.

 

Conclusion

Area and perimeter are two important concepts. They enable us to solve practical problems, plan designs, and measure different shapes with consideration to area and perimeter. It is equally important to understand how to use the formulae for circles, triangles, rectangles and even squares. The knowledge is valuable in our day-to-day life, and not just during examinations. Be it during budgeting as an adult or in planning during school, be ready to tackle geometry and many other measurement-related problems with ease.

 

Frequently Asked Questions on Area and Perimeter

1. What is the formula of area and perimeter?

Ans: The formula for area depends on the shape. For a rectangle, it's:

Area = length × breadth

The formula for perimeter is the total distance around the shape. For a rectangle:

Perimeter = 2 × (length + breadth)

 

2. How do you find the perimeter and area?

Ans: To find the perimeter, add the lengths of all sides of a shape.

To find the area, multiply the relevant dimensions (like length and width for rectangles). Always check which shape you're working with to use the correct formula.

 

3. How to calculate the area?

Ans: To calculate the area, use the shape-specific formula. For example:

• Rectangle: length × breadth

• Triangle: ½ × base × height

• Square: side × side
  
  

4. How to answer area and perimeter?

Ans: First, identify the shape and its dimensions. Then:

• Use the right area formula to find the space inside.

• Use the correct perimeter formula to find the length around it.
  Always write units like cm² for area and cm for perimeter.

 

5. What is the formula for perimeter?

Ans: The perimeter formula depends on the shape. For example:

• Rectangle: 2 × (length + breadth)

• Square: 4 × side

• Triangle: Add all three sides

 

Explore more math topics like this at your own pace and become confident in problem-solving!