How to Find the Perimeter of a Square?

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The square is a special type of rectangle; calculating it is very easy once you know what to do. The square has all 4 sides as equal, which makes it distinct from the normal definition of the rectangle. This article will consider how to calculate the perimeter of a square. Different types of squares will be computed based on the info available to provide students with a sound and complete knowledge of the square perimeter.

The perimeter of the Square formula

The perimeter of a square is the distance around the square. The formula is given as;

P = 4L

Where L is the sides.

The formula is easily explainable. Since the square has four equal sides and the perimeter is simply the addition of all 4 Ls, then it would become;

L + L + L + L = 4L

However, for the above formula to work, at least one of the four sides must be available. In an instance where the four sides are not available, it would be impossible to find the perimeter except

  • If the square area is available
  • If the square is inscribed inside a circle (Inscribed square), the circle radius or diameter is known.

This article will consider all the scenarios with examples to help students understand how to find the perimeter of a square irrespective of the circumstances.

How to calculate the perimeter of a square with examples?

As shown above, calculating the perimeter of a square would depend on the information provided concerning the shape. Below are the three methods to calculate the perimeter of a square.

Method 1: Basic Formula for Calculating the Perimeter of a Square

Step 1: There has to be at least one side of the length available

Step 2: Use the Basic Formula P = 4L

Example 1

Find the Perimeter of the Square with side lengths of 3

Solution.

Since the side lengths are 3

Then the perimeter is

P = 4L

P = 4(30)

P = 12

Method 2: Finding the Perimeter based on information about the Square’s Area

Step 1: Input the Square area into the basic formula: A = L2

Step 2: carry out the computation with the formula in step 2 such that you arrive at L

Step 3: Find the perimeter using the Basic Formula P = 4L

 We will use an example to highlight this method.

Example 2

Find the perimeter of a square whose area is 16.

Step 1: Input the Square area into the basic formula: A = L2

16 = L2

Step 2: carry out the computation with the formula in step 2 such that you arrive at L

16 = L2

L = 4

Step 3: Find the perimeter using the Basic Formula P = 4L

P = 4(4)

P = 16

In this case, the perimeter is the same as the area. However, this is simply coincidental.

Method 3: Finding the perimeter of an Inscribed Square in a Circle when the length is not known but the circle Radius is known

What is an Inscribed Square?

An Inscribed Square is a square inside a circle. Finding the perimeter of this kind of square is usually easy as it follows the normal perimeter formula established in method 1. However, in exams, it is extremely common for the sides of an inscribed square to be hidden while the circle’s radius or diameter is available.

The diameter is the line that dissects a circle into two halves irrespective of the position of a straight line. It is twice the radius. i.e D = 2r

Below is an Inscribed Square

As can be seen from the above-inscribed square, all of the sides are equal. Now, half of the circle is the diameter and twice the radius. Also, cutting through the square from one diagonal end to the other will divide the circle into equal two halves and make the square two right angles. That is

The middle line separating the square D = 2r is the radius. Now, if we consider one of the right-angle triangles, the diameter will be the hypotenuse, the vertical side the length while the bottom side the base.

Using the Pythagoras theorem in such a case will help us find the base and height of the triangle, which will be equal to each other as every side of a square is equal. Finding the base or height of the triangle is the same as finding a side of the inscribed square. Once that is done, the perimeter can then be computed.

An example will be used to explain this method better.

Example 3

Find the perimeter of the inscribed square where the radius of the circle is given as 11

Solution

Step 1: Draft out an inscribed square and divide it into two right angles. Label accordingly afterwards

Step 2: Use Pythagoras to calculate a = b since the hypotenuse is already given as 22

Pythagoras theorem

D2 = a2 + b2

222 = a2 + b2

Since a = b, then a + b = 2a or 2b, we will choose 2a instead

222 = a2 + a2

222 = 2a2

484 = 2a2

484/2 = a2

242 = a2

a = 15.556

this also implies that b = 15.556

Step 3: Calculate the perimeter of the square

Now recall the length and base are simply sides of the square.

Therefore;

P = 4 x L

P = 4 X 15.556

P = 62.224

Conclusion

This article has highlighted the three major types of computations that students will likely face when asked to compute the perimeter of a square. Each type of square was comprehensively covered with detailed explanations and examples. The examples were expertly selected to prepare students for all types of tests they may have to solve.

How to Find the Perimeter of a Square?

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