Perimeter of Square
The perimeter of a square is defined as the total length that its boundary covers. The perimeter of any closed geometrical object is calculated by finding the distance around that object. For a square, the perimeter can be calculated by finding the sum of all the sides. Let us have a look at the article in order to understand the concept in a better way.
What is the Perimeter of Square?
A perimeter of any shape is either a path that encompasses/surrounds/outlines a shape (in two dimensions) or its length (one-dimensional). The perimeter of a square can be calculated by adding the length of all its sides.
Perimeter of Square Formula
The formula to calculate the perimeter of a square is as, mathematically expressed as;
Perimeter of square, (P) = 4 × Side
Example: Calculate the perimeter of a square with each side measuring 7 units.
Solution: Given: Side length of square = 7 units
We know, using the perimeter of a square formula,
Perimeter of square = 4 × Side
⇒ 4 × 7 = 28 units
Derivation of Perimeter of Square Formula
The perimeter of the square is defined as the total length of the boundary of a square. In order to calculate the perimeter of the square, we will find the sum of all of its sides. Since, all the sides of a square are equal, for a square, with each side measuring “s” units, perimeter will thus be given as,
Perimeter of square = s + s + s + s
⇒ Perimeter of square = 4s, where “s” is the side length of the square.
How to Calculate Perimeter of a Square?
The perimeter of the square can be calculated following different methods depending upon the known parameters. This section will cover the method using,
- Side length
- Diagonal
- Area
Perimeter of Square Using Side Length
We generally find the perimeter for this case by multiplication of side length with 4.To find the perimeter of a square using the side length, we can follow the steps given below,
- Step 1: Note down the measurement of the side.
- Step 2: Multiply the noted length with 4.
- Step 3: Express the obtained result with the unit.
Perimeter of Square Using Diagonal
The perimeter of the square can also be calculated if the length of its diagonal is known to us. To find the perimeter of a square using the diagonal, we can follow the steps given below,
- Step 1: Note down the measurement of the diagonal of the square.
- Step 2: Calculate the side length using the diagonal,
Side = diagonal/√2 = √2 × diagonal/ 2 - Step 3: Multiply this obtained value of side length, (√2 × diagonal/ 2) by 4 and express the answer in units,
Perimeter = (√2 × diagonal/2) × 4 = 2√2 × diagonal units.
Perimeter of Square Using Area of Square
We can find the perimeter of the square given the area. To find the perimeter of a square using the area, we can follow the steps given below,
- Step 1: Note down the area of square.
- Step 2: Calculate the side length using the area,
Side = √area - Step 3: Multiply this obtained value of side length, (√area) by 4 and express the answer in units,
Perimeter = (√area) × 4 = 4√area units.
Let us have a look at a few solved examples to understand the perimeter of the square better.
Tricky math problems with the squares:
Type I: Finding side length when only the perimeter is given.
Example 1. If the perimeter of the given square is 12 cm. What will be the length of its side?
Solution: Given, the perimeter of the square is 12 cm.
Let the side length be ‘a’ cm.
We know that, the perimeter of a square = 4 × (side length)
12=4×(a)
a = 3 cm
Type II: Finding sides using square properties.
Example 2.If a = 4 cm in the given square. Find b, c. and d.
Solution: Given that side a = 4 cm.
To find side b, c, and d we use the property of the square which states that all the sides of a square are equal.
Therefore, a = b = c = d = 4 cm
Type III: Finding perimeter when one of the sides is given.
Example 3. One of the sides of a square is 5 cm. What will be its perimeter?
Solution: Given, one side of the square is 5 cm.
We know that, the perimeter of a square = 4 × (side length)
= 4×(5)
= 20 cm
Example 4. The length of a side of the square wooden frame is 5 cm. Find the total length of the wood used in the frame.
Solution: Given, the length of a side of this wooden frame is 5 cm.
As we know, the perimeter of a square = 4× (side length)
= 4 (5)
= 20 cm
Hence, the total length of the wood used is 20 cm.
| Fun FactsSquares are one of the three most basic shapes on the earth. The other two are circles and triangles. |
Properties of square:
· Diagonals of a square (quadrangle) bisect each other
· Diagonals of a square (quadrangle) bisect its angles.
· Diagonals of a square (quadrangle) are perpendicular.
· Opposite sides of a square (quadrangle) are both parallel and equal.
· All four angles of a square (quadrangle) are equal. (Square is 360/4 = 90 degrees, so every angle of a square (quadrangle) is a right angle.)
· The diagonals of a square (quadrangle) are equal.
Perimeter of Square Examples
Example 1: If the perimeter of a square is 64 units, find its side.
Solution:
To Find: Side length of square
Given: Perimeter of square = 64 units
Using the perimeter of a square formula,
Perimeter of square = 4 × side units
Substituting values, we get,
64 = 4 × side
⇒ Side = 64/4 = 16 unitsAnswer: The side length of the given square measures 16 units.
Example 2: The area of a square is given as 225 square units. Using the perimeter of a square formula, calculate its perimeter.
Solution:
To find: Perimeter of given square
Given: Area of square = 225 square units
We know, area of a square = (side)2 square units
⇒ 225 = (side)2
⇒ side = √225 = 15 unitsNow, using perimeter of a square formula,
Perimeter of square, P = 4 × side units
⇒ P = 4 × 15 = 60 unitsAnswer: The perimeter of the given square = 60 units.
1. Each side of a square is 2.5 cm. Find its perimeter.
Solution:
Side = 2.5 cm
Therefore, perimeter of a square = 4 × length of a side
= (4 × 2.5) cm
= 10 cm
2. A rope of length 96 m was used to fence a square garden. What is the length of the side of the garden?
Solution:
Perimeter of the garden = Length of the rope = 96 m
We know that perimeter of a square = 4 × length of a side
So, 4 × length of a side = 96 m
Length of a side = 96/4 m = 24 m
Therefore, length of the one side of the square shape garden is 24 m.
3. Find the perimeter of a square shaped playground whose each side length 12 m.
Solution:
We know a square has four equal sides. So, we can easily calculate the perimeter of a square.
The formula for finding the perimeter of a square is:
P = 4 × length of a side
= 4 × 12 m
= 48 m
4. Each sides of a paper sheet is 14 ft. Find its perimeter.
Solution:
Given: Side length is 14 ft.
Perimeter of a square is = 4 × side
= 4 × 14 ft
= 56 ft
Solved Examples on Perimeter of Square
Question 1: Find the perimeter of a square whose side is 5 cm.
Solution:
Given:
Side, s = 5 cm
The formula to find the perimeter of a square is given by:
The perimeter of Square = 4s units
Substitute the value of ‘s’ in the perimeter formula,
P= 4 × 5 cm
P = 20 cm
Therefore, the perimeter of square = 20 cm
Question 2: Calculate the perimeter of a square having a side of 16 cm.
Solution:
Given,
Side of the square = a = 16 cmPerimeter of a Square = 4a
= 4 × 16
= 64 cmQuestion 3: If the perimeter of a square is 92 cm, find its side.
Solution:
Perimeter = 4 × side
Or, Side of Square = ¼ × perimeter
So, side of the square = 92/4 = 23 cm
Example Question #1 : Calculating The Perimeter Of A Square
A square plot of land has area 256 square yards. Give its perimeter in inches.
Possible Answers:4,608 in
1,296 in
1,152 in
2,592 in
2,304 in
Correct answer:2,304 in
Explanation:The sidelength of a square is the square root of its area – in this case, √256=16 yards. Its perimeter is therefore four times that, or 16×4=64 yards. Multiply by 36 to convert to inches:
64×36=2,304 inches.
Example Question #2 : Calculating The Perimeter Of A Square
Five squares have sidelengths 3, 4, 5, 6, and 7 meters. What is the mean of their perimeters?
Possible Answers:10 m
20 m
25 m
27 m
16 m
Correct answer:20 m
Explanation:Multiply each sidelength by four to get the perimeters – they will be 12, 16, 20, 24, and 28 meters, respectively. The mean will be
(12+16+20+24+28)÷5=100÷5=20 meters
Example Question #3 : Calculating The Perimeter Of A Square
Given Square FGHI, answer the following questions.
Square FGHI represents a small field for a farmer’s sheep. How many meters of fence will the farmer require to completely enclose the field?
Possible Answers:120m
30m
60m
225m
45m
Correct answer:60m
Explanation:This question is a thinly veiled perimeter of a square question. To find the total amount of fencing needed, use the following formula:
P=4∗s
Where P is the perimeter of a square, and s is the length of one side.
P=4∗15meters=60meters
Example Question #4 : Calculating The Perimeter Of A Square
A given square has a side length of 7cm. What is its perimeter?
Possible Answers:Not enough information provided
49cm
28cm
28cm2
49cm2
Correct answer:28cm
Explanation:In order to find the perimeter P of a given square with side length s, we use the equation P=4s. Given s=7cm, we can therefore conclude that P=4(7cm)=28cm.
Example Question #5 : Calculating The Perimeter Of A Square
A given square has an area of 64. What is its perimeter?
Possible Answers:8
16
128
32
Not enough information provided
Correct answer:32
Explanation:We are told that the area A of the square is 64. We know the area of a square is defined as A=s2, where s is the length of the side of the square. We can therefore deduce that 64=s2 and that s=8.
In order to find the perimeter P of a given square with side length s, we use the equation P=4s. Given s=8, we can therefore conclude that P=4(8)=32.
Example Question #6 : Calculating The Perimeter Of A Square
A given square has a side of length 19cm. What is the perimeter of the square?
Possible Answers:76cm
361cm
Not enough information provided
361cm2
76cm2
Correct answer:76cm
Explanation:In order to find the perimeter P of a given square with side length s, we use the equation P=4s. Given s=19cm, we can therefore conclude that P=4(19cm)=76cm.
Example Question #7 : Calculating The Perimeter Of A SquareExplanation:
The length of one side of a square is the square root of the area – or, equivalently, the area raised to the power of 1/2. Here, this is
Example Question #8 : Calculating The Perimeter Of A Square
A square courtyard will have paths running diagonally across it (the paths will form an x). If the length of one of the paths will be 14√2 meters long, what will the perimeter of the courtyard be?
Possible Answers:14meters
56meters
64meters
36meters
Correct answer:56meters
Explanation:A square courtyard will have paths running diagonally across it (the paths will form an x). If the length of one of the paths will be 14√2 meters long, what will the perimeter of the courtyard be?
To find the perimeter of a square, we need to find the side lengths. We can find the side lengths from the diagonal by recalling that the diagonal of a square creates two 45/45/90 triangles.
A 45/45/90 triangle has the following side-length ratios: 1/1/√2
This means that if our hypotenuse is 14√2 meters long, our other two sides will be 14 meters long
So our side-length is 14 meters, find the perimeter via the following
P=4s=14∗4=56meters]
Example Question #9 : Calculating The Perimeter Of A Square
A square is created from joining two equilateral triangles of side length = 4m What is the perimeter of the square?
Possible Answers:8m20m16m16m220m2Correct answer:16m
Explanation:Draw yourself a picture for this problem. If you create a square out of two triangles, they meet at the diagonal of the square. Since, we know the triangles are equilateral, then all of the side lengths of the triangle and square are equal. Therefore, we just take the side length and add that four times.
4m+4m+4m+4m=16m
Example Question #5 : Quadrilaterals
A circle with a radius 2 in is inscribed in a square. What is the perimeter of the square?
Possible Answers:32 in
16 in
24 in
12 in
28 in
Correct answer:16 in
Explanation:To inscribe means to draw inside a figure so as to touch in as many places as possible without overlapping. The circle is inside the square such that the diameter of the circle is the same as the side of the square, so the side is actually 4 in. The perimeter of the square = 4s = 4 * 4 = 16 in.
Example Question #2 : How To Find The Perimeter Of A Square
Square X has 3 times the area of Square Y. If the perimeter of Square Y is 24 ft, what is the area of Square X, in sq ft?
Possible Answers:54
108
112
72
144
Correct answer:108
Explanation:Find the area of Square Y, then calculate the area of Square X.
If the perimeter of Square Y is 24, then each side is 24/4, or 6.
A = 6 * 6 = 36 sq ft, for Square Y
If Square X has 3 times the area, then 3 * 36 = 108 sq ft.
Example Question #3 : How To Find The Perimeter Of A Square
A square has an area of 36in2. If the side of the square is reduced by a factor of two, what is the perimeter of the new square?
Possible Answers:32 in.
12 in.
16 in.
48 in.
24 in.
Correct answer:12 in.
Explanation:The area of the given square is given by A=s2 so the side must be 6 in. The side is reduced by a factor of two, so the new side is 3 in. The perimeter of the new square is given by P=4s=4⋅3=12in.
Example Question #4 : How To Find The Perimeter Of A Square
A square garden has an area of 64 square feet. If you add 3 feet to each side, what is the new perimeter of the garden?
Possible Answers:121
25
32
20
44
Correct answer:44
Explanation:By finding the square root of the area of the garden, you find the length of one side, which is 8. We add 3 feet to this, giving us 11, then multiply this by 4 to get 44 feet for the perimeter.
Example Question #5 : How To Find The Perimeter Of A Square
The area of the shaded region of a square is 18. What is the perimeter of the square?
Possible Answers:28
24
36
20
Correct answer:24
Explanation:The area of the shaded region, which covers half of the square is 18 meaning that the total area of the square is 18 x 2, or 36. The area of a square is equal to the length of one side squared. Since the square root of 36 is 6, the length of 1 side is 6. The perimeter is the length of 1 side times 4 or 6 x 4.
Example Question #6 : How To Find The Perimeter Of A Square
The area of a square is 25cm2. If the square is enlarged by a factor of 2, what is the perimeter of the new square?
Possible Answers:80 cm
75 cm
100 cm
40 cm
50 cm
Correct answer:40 cm
Explanation:The area of a square is given by A=s2 so we know the side is 5 cm. Enlarging by a factor of two makes the new side 10 cm. The perimeter is given by P=4s, so the perimeter of the new square is 40 cm.
Example Question #1 : How To Find The Perimeter Of A Square
A square has a side length of s=4in. Find its perimeter.
Possible Answers:12in
8in
Not enough information to solve
16in2
16in
Correct answer:16in
Explanation:In order to find the perimeter of a square, one must add up all of its side lengths. The side lengths of a square are all equal; therefore, the formula for the perimeter of a square is P=4s.
P=4∗4in
P=16in
Remember perimeter should be expressed in single units not units squared. Thus, 16in2 is an incorrect answer.
Example Question #7 : How To Find The Perimeter Of A Square
The diagonal of a square has a length of 10 inches. What is the perimeter of the square in inches squared?
Possible Answers:6√2
20√2
5√2
10√2
Correct answer:20√2
Explanation:Using the Pythagorean Theorem, we can find the edge of a side to be √50, by 2a2=102. This can be reduced to 5√2. This can then be multiplied by 4 to find the perimeter.
Example 1: Find the area and perimeter of the square whose side length is 4 meters.
Solution:
Given that:
a = 4m
Area of square = a2 = 4 × 4 = 16 m2
Perimeter of the square = 4 × 4 = 16 mExample 2: Find the perimeter of square whose sides are 16 cm in length.
Solution:
Perimeter of the square:
P = 4a
P = 4 × 16 cm
P = 64 cm
Hence, the perimeter of square is 64 cm.Example 3: What is the perimeter of a square, if the length of each side is 13 ft?
Solution:
The length of each side of a square is 13ft.
The perimeter of a square:
P = 4 × a
P = 4 × 13
P = 52 ft
The perimeter of the square is 52 ft.Example 4: The perimeter of a square is 24 cm. What would the length of its sides be, if its perimeter is increased by 4 cm?
Solution:
New perimeter of the square = 24 + 4 = 28 cm.
New perimeter of the square = 4 × the new length of a side of the square
Let the new length of a side of the square = l cm
a = 7 cmExample 5: The area of a square park is 225 m2. Find its perimeter.
Solution:
Given:
Since the area is 225 m2, the length of the sides can easily be determined:
A = s²
225 = s²
s = 15m
Thus, the perimeter of park is:
P = 4 × s.
P = 4 x 15 m.
P = 60 m.Example 6: Find the perimeter of the square, whose side length is 9.2 meters.
Solution:
Given: Side length (a) = 9.2 meters
Perimeter of the square = 4 × a
= 4 × 9.2
Perimeter of the square = 36.8 meters.FAQs on Perimeter of Square
What is Perimeter of Square in Math?
The perimeter of a square in math is the total length that its boundary. The perimeter formula for square is expressed as the sum of all the sides. It is represented as P = 4 × side units.
What is the Formula of Perimeter of Square?
The perimeter of a square is defined as the length that its boundary covers. The formula to calculate the perimeter of a square is given as: P = 4 × side.
How to Find Perimeter of Square?
The perimeter of a square can be calculated by finding the total sum of all its sides. Since, the measure of all the sides of a square is equal, to calculate the perimeter of a square we can simply multiply 4 with its side length.
How to Find the Side Length of a Square When the Perimeter is Given?
The perimeter of a square is given as, P = 4 × side. On rearranging the above formula to calculate the side length of the square when the perimeter is given, we get, side = P/4. Therefore, the side length of a square can be calculated by dividing the given perimeter by 4.
How to Find Perimeter of Square When Area is Given?
The area of a square can be calculated using the formula, area = side × side. On rearranging this formula to calculate the side length of the square using the area, we get, side = √area. Since the perimeter of a square is given as: 4 × side, we can calculate the perimeter of a square when the area is given using the formula: 4√area.
What is the Unit of Perimeter of Square?
The perimeter of a square is the total distance around its boundary, or the lengths of its sides added together. Perimeter (P) is measured in units such as inches(in), yards(yd), millimeters(mm), centimeters(cm), and meters(m).
How to Use the Perimeter of Square Calculator?
Perimeter of square calculator is used to do fast calculations and get the desired answer of the perimeter of square quickly. To calculate the perimeter of a square using a calculator we need to enter certain specific parameters such as the side length of a square.
How to Find Perimeter of Square When Diagonal is Given?
The diagonal of a square is given as, √2 × side. Rearranging this formula to calculate the side of the square, we get, side = diagonal/√2 = (√2 × diagonal)/2 . Thus, the perimeter of the square can be calculated using the formula, P = 2√2 × diagonal.
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