# Perimeter of a Square – Formula, Derivation, Examples, Practice Problems

Updated on January 5, 2024

Welcome to another fun-filled mathematical adventure with Brighterly, your trusted partner in making math easy and enjoyable for children. We pride ourselves in crafting engaging, kid-friendly content that transforms learning into an exciting journey of discovery.

In today’s post, we dive into a fundamental concept in geometry – the perimeter of a square. We’re going to explore this topic in depth, unraveling its formula, deriving it, and applying it in a variety of examples. We’ll also provide practice problems to test your understanding and improve your skills.

## What is the Perimeter of a Square?

In mathematics, the perimeter is the path or distance that surrounds a two-dimensional shape. For a square, one of the most regular geometric shapes, the perimeter is simply the total length of its four equal sides. So, if we denote the side length as ‘a’, the perimeter of a square would be 4 times the length of one side, or 4*a. This is a fundamental concept you can learn in geometry.

## Derivation of Perimeter of Square Formula

Let’s delve into the derivation of the perimeter of a square formula. A square has four equal sides. If we label one side ‘a’, then the total length of the four sides, which gives us the perimeter, is simply 4*a. This comes directly from the definition of a square as a shape with four equal sides.

## How to Find the Perimeter of a Square?

To find the perimeter of a square, you need to know the length of one of its sides. Simply multiply this length by four. Why four? Because a square has four sides, and each side has the same length! You can learn more about this on the properties of squares page.

## Perimeter of Square Using Side Length

In other words, the perimeter of a square using the side length is as straightforward as taking the given side length (a) and multiplying it by 4. If your square has a side length of 5 units, for instance, the perimeter would be 4*5, which equals 20 units.

## Perimeter of Square Using Diagonal

If you’re given the diagonal instead, you can still find the perimeter of a square. The diagonal (d) of a square relates to the side length (a) by the formula a = d/√2. Hence, you can use the diagonal to find the side length, and then calculate the perimeter as above.

## Perimeter of Square Using Area of Square

Perhaps you know the area of the square but not the side length or the diagonal. Don’t worry! The side length (a) is the square root of the area (A). So, you can find ‘a’ using the area and then find the perimeter.

## Perimeter of a Square Formula

To summarize, here’s the perimeter of a square formula:

If ‘a’ is the side length, Perimeter = 4*a.

If ‘d’ is the diagonal, Perimeter = 4*(d/√2).

If ‘A’ is the area, Perimeter = 4*√A.

## Finding Perimeter of a Square when the Side is Unknown

To find the perimeter of a square when the side length is unknown, you might be given either the diagonal or the area. Use the appropriate formulas mentioned above to first find the side length, and then calculate the perimeter.

## Solved Examples On Perimeter of a Square

Let’s go through a few solved examples on the perimeter of a square. Suppose the side length is 7 units. Then the perimeter is 4*7 = 28 units. If the diagonal is given as 10 units, then the side length would be 10/√2 ≈ 7.07 units. So, the perimeter would be about 28.28 units.

## Practice Problems On Perimeter of a Square

Ready for some practice problems on the perimeter of a square? Here they are:

- If the side length of a square is 6 units, what is the perimeter?
- If the diagonal of a square is 8 units, what is the perimeter?
- If the area of a square is 25 square units, what is the perimeter?

## Conclusion

Understanding the perimeter of a square is not just a fundamental skill in geometry, but it’s also a stepping stone to grasping more complex mathematical concepts. This foundation serves as a useful tool when delving into other areas like algebra, trigonometry, and calculus. Remember, whether you know the side length, diagonal, or area of a square, you can still calculate the perimeter!

At Brighterly, our mission is to make math engaging, accessible, and enjoyable for kids. We firmly believe that when mathematics is presented in a friendly and relatable manner, it becomes less of a daunting task and more of an intriguing puzzle to be solved. We want to inspire curiosity and create an environment where learning is not a chore, but an adventure.

## Frequently Asked Questions On Perimeter of a Square

### What is the perimeter of a square?

The perimeter of a square is the total length of its four equal sides. Imagine you’re walking along the edge of a square-shaped park. The distance you would cover from the point you start, going around the park and coming back to where you started is the perimeter of that square park.

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

The most straightforward way to find the perimeter of a square is by knowing the length of one side. Since all sides of a square are equal, you simply multiply the length of one side by four. However, even if you don’t know the side length, you can still calculate the perimeter if you know the diagonal or the area of the square. The diagonal helps you derive the side length by dividing it by the square root of 2, and the area of a square allows you to find the side length by taking the square root of the area. With either derived side length, you can then find the perimeter by multiplying it by four.

### Can you find the perimeter of a square with just the area?

Absolutely! If you have the area of the square, you can find the side length by taking the square root of the area. For example, if the area of a square is 16 square units, the side length would be √16, which equals 4 units. Then, to get the perimeter, you multiply the side length by four, giving you a perimeter of 16 units for this square. Thus, even with just the area, you can calculate the perimeter of a square.