Perimeter of Square: Formula, Examples and Questions

Perimeter of Square is the total length of its four equal sides. This page covers the perimeter of square formula, reverse calculations from perimeter or area, unit conversions, common perimeter of square questions, and short methods for solving perimeter of square problems accurately.

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What Is the Perimeter of a Square?

The perimeter of a square is the total distance around its boundary. Since all four sides of a square are equal, its perimeter is four times the length of one side.

If the side of a square is a, then the perimeter is P = 4a. Perimeter is measured in linear units such as centimetres, metres or kilometres. For example, a square with side 8 cm has perimeter 4 × 8 = 32 cm.

Perimeter of Square Video Lessons

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15 Lessons
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Square Area and Perimeter

Learn how to calculate the area and perimeter of a square using the relevant side-length formulas, with clear application of both mensuration concepts.

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Perimeter of Square Formula & Tricks

Important Formulas

Perimeter of a square
P = 4a

P is the perimeter and a is the length of one side.

Side from perimeter
a = P ÷ 4

Divide the given perimeter by 4 to find the side length.

Perimeter from area
P = 4√A

If the area is A, the side is √A, so the perimeter is 4√A.

Perimeter from diagonal
P = 2d√2

If the diagonal is d, then the side is d/√2 and the perimeter is 2d√2.

Quick Tricks

Multiply the side by four

A square has four equal sides, so calculate its perimeter directly as 4 × side.

Example: For side 13 m, P = 4 × 13 = 52 m.
Find the side before calculating perimeter

When area is given, first take its square root to obtain the side, then multiply by 4.

Example: If area = 196 cm², side = √196 = 14 cm and perimeter = 4 × 14 = 56 cm.
Keep perimeter units linear

Do not write square units for perimeter. Convert all side measurements to the same unit before applying P = 4a.

Example: For side 2.5 m, perimeter = 10 m, not 10 m².

Perimeter of Square Concepts

Using the Perimeter of Square Formula

The perimeter of a square is found by multiplying its side length by 4: P = 4a.

The four sides are equal, so adding them gives a + a + a + a = 4a. If the side is 6.5 cm, then P = 4 × 6.5 = 26 cm.

Example: Side = 9 m; perimeter = 4 × 9 = 36 m.

Finding the Side from a Given Perimeter

To find the side length, divide the perimeter by 4: a = P/4.

This reverse formula follows from P = 4a. If the perimeter is 84 cm, then each side is 84 ÷ 4 = 21 cm.

Example: Perimeter = 72 m; side = 72 ÷ 4 = 18 m.

Finding Perimeter When Area Is Given

For a square with area A, the side is √A and the perimeter is 4√A.

The area of a square is A = a². Therefore, a = √A. For area 225 m², the side is √225 = 15 m, so the perimeter is 60 m.

Example: Area = 324 cm²; side = √324 = 18 cm; perimeter = 4 × 18 = 72 cm.

Finding Perimeter When the Diagonal Is Given

If the diagonal is d, the perimeter is P = 2d√2.

For a square, diagonal d = a√2. Hence a = d/√2, and P = 4d/√2 = 2d√2. If d = 7√2 cm, then P = 2 × 7√2 × √2 = 28 cm.

Example: Diagonal = 10√2 cm; perimeter = 2 × 10√2 × √2 = 40 cm.

Units and Comparison of Perimeters

Perimeter must be expressed in linear units, and all lengths must use the same unit before calculation.

Use 1 m = 100 cm and 1 km = 1000 m. If two squares have sides a and b, their perimeter difference is 4|a − b|.

Example: For sides 3 m and 250 cm, convert 250 cm to 2.5 m. The perimeter difference is 4(3 − 2.5) = 2 m.

Perimeter of Square Visual Guide

Use the diagram or chart below to understand the concept clearly.

Square with Equal Side Lengths

Visual guide: Square with Equal Side Lengths
Top side: a Right side: a Bottom side: a Left side: a
A square has four equal sides, so its perimeter is a + a + a + a = 4a.

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Practice Perimeter of Square Questions

Practise published questions related to this topic.

1Simplify: 4 - [6 - {14 - (10 - overline{8 - 6})}]→ 2A seller buys 240 Television. He sells some of them at a gain of 20% and the remaining at a gain of 30%. If he gains 28% on the whole, then how many did he sell at a gain of 20%?→ 3The LCM of two numbers 216 and 120 is 1080. Find the HCF of these numbers.→ 4Three persons Amar, Akbar and Sunil start a business with the investments ₹15,600, ₹ 10,400 and ₹ 11,700, respectively. They got 20% of the total investment as profit and they planned to reinvest 5% of the profit. If the remaining profit is distributed in the ratio of their investments, then find the share of Sunil in the profit.→ 596 + (19 of 2) - 38 + 42 ÷ 6 + 28 - 16 = ?→ 6A store has a scheme: 'Buy items worth ₹2,000, get ₹500 off'. If someone buys items worth ₹4,000, what is the effective discount percentage?→ 71/30 is what percentage of 2/60?→ 8If x = {(√5 + √3)/(}{√5 - √3)} + ({√5 - √3)}/({√5 + √3)} , then the value of x is:→ 9A typist takes 40 minutes to type 2 pages. How long (in minutes) will he take to type 104 pages?→ 10An 8-digit number is divisible by 45. If the digits are rearranged, then the number must be divisible by:→

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Perimeter of Square Quick Quiz

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Quick Revision Notes

Perimeter of Square Revision Points

Use these formulas and rules for quick revision.

  • Perimeter of a square: P = 4a.
  • Side from perimeter: a = P/4.
  • If area is A, side = √A and perimeter = 4√A.
  • If diagonal is d, perimeter = 2d√2.
  • Perimeter uses linear units, such as cm, m or km.
  • Convert all given lengths to the same unit before calculating.
  • A square with side increased by x has perimeter increased by 4x.
  • For two squares with sides a and b, the difference in perimeters is 4|a − b|.

Related Topic Explainers

Area of Square →

Perimeter of Square FAQs

What is the perimeter of square formula?

The formula is P = 4a, where a is the side length of the square.

What is the perimeter of a square with side 15 cm?

P = 4 × 15 = 60 cm.

How do you find the side of a square when its perimeter is 100 m?

Divide the perimeter by 4: side = 100 ÷ 4 = 25 m.

What is the perimeter of a square with area 256 cm²?

Side = √256 = 16 cm. Therefore, perimeter = 4 × 16 = 64 cm.

What is the perimeter of a square when its diagonal is 12√2 cm?

Use P = 2d√2. Thus, P = 2 × 12√2 × √2 = 48 cm.

What unit is used for the perimeter of a square?

Perimeter is measured in linear units, such as cm, m or km. Square units such as cm² are used for area, not perimeter.

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