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Area of Square

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Area of a Square or area of any figure is defined as the space occupied by it in 2-D space. So, Area of Square is defined as the space enclosed by the boundary of the square. Measurement of area is done in square units. The SI unit for measurement of the area is m2.

For finding areas of various figures, several pre-defined formulas are used, in this article, we will study the formulas for finding the area of the square.

What is Square?

Square is a type of quadrilateral (polygon with four sides) with all four sides and angles being equal.

Some common properties of square are:

  • All four sides of a square are of equal length.
  • Each internal angle of a square measures 90 degrees.
  • Diagonals of a square intersect each other at right angles and bisect each other, dividing the square into four congruent right-angled triangles.
  • Diagonals of a square are equal in length.
  • A square has rotational symmetry of order four, meaning it looks the same after a rotation of 90°, 180°, or 270°.

Area of Square

Space enclosed inside the boundaries of any figure is called the area of the figure. It is a physical quantity that gives us the idea of how much space is covered by an object.

Square is a Two-Dimensional (2D) figure that has 4 sides of equal lengths. The area of a square concept comes under the topic of mensuration which deals with the measurements of Two Dimensional and Three Dimensional figures. Length, Perimeter, Area, Volume, etc. come under the measurements of a figure. 

Area of a square is calculated by multiplying its sides by its sides, i.e. finding its sides square.

Area-of-Square

Area of Square Definition

Area is region inside boundaries of an object. Area of a square is defined as number of square units needed to fill square. To calculate square’s area we need to know the length of any of its sides. The area of the square can be calculated by squaring the length of any of its sides. 

Area Formula for Square

Various formula for finding the area of a square is listed below,

Area of Square = Side2 unit2

Square

Area can be measured in various units, some of the conversions for changing standard units of the area to other desired units are given below:

1 m2 = 10000 cm2

1 km2 = 1000000 m2

If required in calculation we can find the perimeter of the square by the given formula

Perimeter of Square = 4 × sides units

Let’s consider an example to understand the use of formula for area of square.

Example: What is Area of a square if each side of length is 4cm?

Solution:

Given,

  • Side length (s) = 4 cm

Area of Square = s2 = 42 = 16 cm2

Area of square with side length 4 cm is 16cm2

Area of Square using Diagonals

Area of Square when the diagonal length is given,

Area = (1/2) × d2

Where, d is Length of Diagonal.

Area of Square using Diagonals

Example: Find Area of a square if the length of the diagonal is 6cm.

Solution:

Given,

  • Diagonal length (d) = 6 cm

Area = (1/2) × d2

⇒ Area = (1/2) × 62

⇒ Area = 36/2 = 18cm2

Area of square is 18cm2.

Area of Square Using Perimeter

We can find an area if perimeter of a square is given.

Formula of the perimeter of a square = 4 × side

From the above formula, we can find the side length by dividing the Perimeter by 4.

Side length(s) = Perimeter/4

Using side length we can find the area of the square by using the formula Area = side ×  side = (Perimeter/4)2.

Area of Square Using Perimeter

Example: Find Area of the Square if the perimeter of a square is 36 cm.

Solution:

Given,

  • Perimeter = 36 cm

So, Side length=perimeter/4

Side(s) = 36/4 = 9 cm

From the side length we can calculate area of square by

Area = Side2 = 92 = 81 cm2

Area of square with perimeter 36 cm  is 81 cm2.

How to Find Area of Square?

Area of square can be calculated if the dimensions of the square are known. We can calculate the area of the square by various formulas depending on the initial values that are given.

Follow the steps given below to find the area of the square.

Step 1: Note the dimension of the square given. For example to find the area of a square with a side of 10 m. The given dimension (side) is 10 m.

Step 2: Use the area of the Square formula. As Area of Square = (Side)2. For given example,

  • Area of Square = (10)2

Step 3: Simplify the value obtained in step 2. For given example,

  •  Area of Square = (10)2 = 100

Step 4: Add unit2 as the unit to the answer obtained in step 3 to get the final answer. For given example,

  • Area of Square = 100 m2

Area of a Square: Summary

All the formulas discussed in the article are:

Formula Description
Area = s2 Area of a square using side length (s).
Area = (1/2) × d2 Area of a square using diagonal length (d).

Area of Square = (Perimeter/4)2

Area of Square using Perimeter.

Related Articles:

Examples on Area of Square

Example 1: Find Area of the Square if the perimeter of a square is 64cm.

Solution:

Given,

  • Perimeter = 64cm

So, Side length = perimeter/4

Side(s) = 64/4 = 16cm

From the side length we can calculate area of square by

Area =Side2

Area = 162 = 256 cm2

Area of square with perimeter 64cm  is 256cm2.

Example 2: Find area of a square if the length of the diagonal is 12cm.

Solution:

Given,

  • Diagonal length (d) = 12 cm

Area = (1/2) × d2

Area = (1/2) × 122

Area = 144/2 = 72 cm2

Area of square is 72 cm2.

Example 3: Length of each side of a square is 5cm and the cost of painting it is Rs. 5 per sq. cm. Find total cost to paint the square.

Solution:

Given,

  • Side length (s) = 5cm

Area of Square = s2

A = 52 = 25 cm2

For 1 sq.cm cost of painting is Rs 5.

Total Cost of painting the 25sq cm= 25 × 5 = Rs125

Example 4: A floor that is 60 m long and 30 m wide is to be covered by square tiles of side 6 m. Find the number of tiles required to cover the floor.

Solution:

Length of the floor = 60 m

Breadth of the floor = 30 m

Area of floor = length × breadth = 60 m × 30 m = 1800 sq. m

Length of one tile = 6 m

Area of one tile = side ×side = 6 m  × 6 m = 36 sq. m

No. of tiles required = (area of floor)/(area of one tile) = 1800/36  = 50 tiles

Total tiles required is 50

Example 5: What is Area of a Square if perimeter of a square is 24 cm?

Solution:

Given,

  • Perimeter = 24 cm

So, Side length = perimeter/4

Side(s) = 24/4 = 6cm

From the side length we can calculate area of square by

Area = Side2

Area = 62 = 36cm2

Area of square with perimeter 24 is 36cm2.

Area of a Square Worksheet

Attempt the below area of a square quiz:

P1: If a square has a side length of 8 meters, what is its area?

P2: A square has an area of 49 square centimeters. What is the length of one side of the square?

P3: If the area of a square is 144 square inches, what is the length of its side?

P4: What is the area of a square with a perimeter of 20 meters?

P5: If the area of a square is 100 square feet, what is the length of its diagonal?

P6: A square field has an area of 2500 square meters. What is the length of one of its sides?

P7: Diagonal of a square is 10√2 centimeters. What is the area of the square?

P8: If the area of a square is 121 square centimeters, what is the length of its diagonal?

P9: Area of a square is 169 square units. What is the perimeter of the square?

P10: A square garden has an area of 400 square feet. What is the length of one of its sides?

Area of a Square with Perimeter

P1: A square has a perimeter of 24 meters. What is its area?

P2: If the perimeter of a square is 40 centimeters, what is the area of the square?

P3: Given that the perimeter of a square is 60 units, what is the area of the square?

Area of a Square by Diagonal

P1: Diagonal of a square measures 10 centimeters. What is the area of the square?

P2: If the diagonal of a square is 12 inches, what is the area of the square?

P3: A square has a diagonal length of 16 meters. What is its area?

Area of a Square Inscribed in a Circle

P1: If a square is inscribed in a circle with a radius of 5 units, what is the area of the square?

P2: A square is inscribed in a circle with a diameter of 10 centimeters. What is the area of the square?

P3: Given a circle with a radius of 8 units, find the area of the square inscribed within it.

Area of a Square Pyramid

P1: Base of a square pyramid has a side length of 6 meters, and its height is 8 meters. What is the surface area of the pyramid?

P2: If the base of a square pyramid has an area of 36 square feet and its height is 9 feet, what is the total surface area of the pyramid?

P3: A square pyramid has a base area of 64 square centimeters and a height of 10 centimeters. What is the total surface area of the pyramid?

FAQs on Area of Square

What is Area of Square?

Area of a square is defined as the total number of units of a square that is enclosed by the boundary of a square. i.e. it is defined as the space occupied by the square in the 2-D plane.

What is Formula for Area of a Square?

A square is a quadrilateral with all four sides equal. Its area can be calculated with formula Sides square, i.e. 

Area of Square = side × side square units

What is Unit for Measuring Area of a Square?

Area of square is measured in square units i.e. square m, square cm, etc.

What is Area of Square when a Diagonal is Given?

Suppose diagonal of a square is given, then the formula to find the area of a square is given by:

Area = (½) × d2 square units

How to Find Area of Square Pyramid?

Area of square is found using the formula Area = (s)2, where s is side of square pyramid.

How Area of Square is Derived?

Area of Square is derived as, we know area of square when diagonal is given,

Area = (½) × d2

Using Pythagoras Theorem,

d = √2(a)

Area = (½) × (√2a)2

Area = ½ × 2a2 = a2

Thus, area of square is derived

How to find Area of a Square Pyramid?

Area of a square pyramid is calculated using formula,

Area of square = a2 + 2a√[(a/2)2 + h2]



Last Updated : 14 Mar, 2024
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