# Area and Perimeter – Definition with Examples

Created on Dec 17, 2023

Updated on January 15, 2024

Welcome to another enlightening post from Brighterly, your trusted guide in making learning easy and enjoyable for children. Today, we embark on an adventure into the world of geometry, exploring the fascinating concepts of Area and Perimeter. Why are these concepts important, you ask? Well, area and perimeter form the bedrock of our understanding of space and distance, influencing everything from architectural design to artwork. By the end of this post, you’ll be able to identify, understand, and calculate the area and perimeter of different geometric shapes, enhancing your mathematical knowledge and application. Let’s dive right in!

## What is Area?

Area is an expression of the extent or size of a surface. It’s a mathematical concept that helps us understand the space within the boundaries of a flat, two-dimensional shape, like a rectangle, square, circle, or triangle. In simpler terms, when we talk about area, we refer to the size of the ‘playground’ inside a shape where actions can take place.

From a farmer wanting to know the extent of his farmland to a child wishing to calculate the size of her drawing paper, understanding area has real-world implications. Let’s look at it this way: if you want to paint a wall, the amount of paint you would need directly depends on the area of the wall. A wall with a larger area would require more paint, right? To make it even simpler, imagine your favourite cookie. The area of that cookie is the space the delicious goodness covers on your plate! You can learn more about the concept of area here.

## What is Perimeter?

If area covers the extent within a shape, what do you think perimeter is? Here’s a hint: take a car and drive around the boundaries of a city. The total distance you’ve covered by the time you complete a full circle is somewhat like the concept of perimeter in mathematics.

So, the perimeter is the total distance around the edges of a two-dimensional shape. Whether it’s a square, a rectangle, or any other polygon, the perimeter gives you the length of its boundary. When you tie a string around your wrist to make a bracelet, the length of the string you need is the perimeter of your wrist. Similarly, when you walk around a playground, the total distance you walk is the perimeter of the playground.

## What is the Difference Between Area and Perimeter?

While both area and perimeter deal with measurements related to a shape, they’re not the same. If we imagine our shape to be a playground, the area tells us how much space there is to play inside it, while the perimeter tells us how long the fence around the playground is.

In practical terms, if you wanted to put up a fence around your garden, you’d need to know the perimeter, but if you wanted to sow seeds, the area is what you’d need. The main difference, then, lies in what each measures: area measures the space inside the shape, and perimeter measures the boundary around it.

## Area and Perimeter For all Shapes

Different shapes have unique ways of calculating area and perimeter. A square’s calculations differ from those of a rectangle, which in turn differ from a triangle’s, and so on. But the underlying concepts of area (space inside) and perimeter (length around) remain the same. Let’s understand these concepts with examples for a rectangle, square, triangle, and circle.

If you want to improve your child’s mastery of perimeter and area, we recommend that you check out Brighterly’s worksheets. They can significantly improve your child’s math skills.

## Perimeter and Area of a Rectangle

A rectangle is a quadrilateral with opposite sides equal. Its area is calculated by multiplying its length and breadth (Area = length x breadth). If you have a rectangular room that’s 10 feet long and 6 feet wide, the total area of your floor (where you could lay a carpet, for example) would be 60 square feet.

The perimeter of a rectangle is the sum of the lengths of all its sides. For a rectangle, this is 2 times the sum of its length and breadth (Perimeter = 2(length + breadth)). So the perimeter of the same room would be 2(10+6) = 32 feet.

## Perimeter and Area of a Square

A square is special because all its sides are equal. To find the area of a square, you just need to square the length of one side (Area = side^2). So if each side of a square playground is 20 feet, the total area would be 400 square feet.

The perimeter of a square is four times the length of one side (Perimeter = 4 x side). The perimeter of the same square playground would be 4 x 20 = 80 feet.

## Perimeter and Area of Triangle

A triangle has three sides. To calculate the area of a triangle, you multiply the base by the height and then divide by 2 (Area = 1/2(base x height)). If you have a triangle with a base of 8 feet and a height of 5 feet, the area would be 1/2(8 x 5) = 20 square feet.

The perimeter of a triangle is the sum of the lengths of its three sides. If our triangle has sides of 8 feet, 5 feet, and 7 feet, the perimeter would be 8 + 5 + 7 = 20 feet.

## Area and Circumference of Circle

A circle’s area is given by the formula Area = π(radius^2), where π (Pi) is a mathematical constant approximately equal to 3.14, and the radius is the distance from the center of the circle to its boundary. If you have a circular pond with a radius of 7 feet, the area would be π(7^2) = 153.94 square feet.

The perimeter of a circle, better known as the circumference, is calculated as Circumference = 2π(radius). The circumference of the same pond would be 2π(7) = 43.96 feet.

## Area and Perimeter Formulas

It’s crucial to remember the formulas to calculate area and perimeter for various shapes. These formulas provide a consistent way to measure the space within (area) and around (perimeter) different geometrical shapes.

Square:

- Area = side^2
- Perimeter = 4 x side

Rectangle:

- Area = length x breadth
- Perimeter = 2(length + breadth)

Triangle:

- Area = 1/2(base x height)
- Perimeter = side1 + side2 + side3

Circle:

- Area = π(radius^2)
- Circumference = 2π(radius)

## Calculating Area and Perimeter for Different Shapes

To further understand the calculation of area and perimeter, let’s work through examples for each shape mentioned above.

### Triangle

Given a triangle with a base of 10 units, a height of 6 units, and sides measuring 10 units, 8 units, and 7 units:

- Area = 1/2(base x height) = 1/2(10 x 6) = 30 square units
- Perimeter = side1 + side2 + side3 = 10 + 8 + 7 = 25 units

### Square

Given a square with each side measuring 5 units:

- Area = side^2 = 5^2 = 25 square units
- Perimeter = 4 x side = 4 x 5 = 20 units

### Rectangle

Given a rectangle with a length of 9 units and a breadth of 4 units:

- Area = length x breadth = 9 x 4 = 36 square units
- Perimeter = 2(length + breadth) = 2(9 + 4) = 26 units

## Practice Problems on Area and Perimeter

It’s now time for you to apply these concepts and formulas. Can you solve the following problems?

- What is the area and perimeter of a rectangle with a length of 7 units and a breadth of 3 units?
- What is the area and perimeter of a square with each side measuring 8 units?
- What is the area and perimeter of a triangle with a base of 6 units, a height of 4 units, and sides measuring 6 units, 5 units, and 4 units?
- What is the area and circumference of a circle with a radius of 5 units?

## Conclusion

At Brighterly, we’re committed to making learning an exciting journey, not a chore. We hope that through this in-depth exploration of area and perimeter, we’ve lit up the path of geometry a little brighter for you. It’s fascinating, isn’t it, to realize how these mathematical principles influence our everyday decisions – like choosing the right size of carpet for a room or calculating the amount of fencing required for a garden. Remember, every complex problem can be broken down into simpler parts and solved step by step, just like we did with these geometrical calculations. Keep practising, stay curious, and always continue to learn. Until next time, happy learning with Brighterly!

## Frequently Asked Questions on Area and Perimeter

### What is the formula for the area of a rectangle?

The formula for the area of a rectangle is ‘length x breadth.’ To find the area, you need to measure the length and breadth of the rectangle. Multiply these two measurements together, and you’ll have the area of the rectangle. For example, if you have a rectangular room that’s 10 feet long and 8 feet wide, the area of your room would be 80 square feet.

### How do you find the perimeter of a square?

To find the perimeter of a square, you multiply the length of one side by 4. This formula is derived from the fact that a square has four equal sides. If each side of the square measures 5 units, the perimeter would be 20 units. Remember, the perimeter represents the total distance around the shape. So, if you walked around the edges of this square, you would travel a total distance of 20 units.

### What’s the difference between area and perimeter?

Area and perimeter are two different ways of measuring a shape, but they measure different things. The area measures the space inside a shape. It answers the question, “How much space does this shape cover?” The perimeter, on the other hand, measures the distance around the shape. It answers the question, “How long is the boundary of this shape?” For example, if you were planning a garden, the area tells you how much space you have for planting, while the perimeter tells you how much fencing you’d need to enclose the garden.