Area Of Square Given Perimeter

Area of Square

The area of a square is defined every bit the number of square units needed to fill this shape. In other words, when we desire to find the expanse of a square, we consider the length of its side. Since all the sides of the shape are equal, its area is the product of its ii sides. The mutual units used to measure the area of the foursquare are square meters, square anxiety, square inch, and foursquare cm.

The expanse of a square tin can also exist calculated with the help of other dimensions, such as the diagonal and the perimeter of the foursquare. Let us try to understand more about the surface area of the square on this folio.

1.	What is the Area of Square?
2.	Surface area of a Square Formula
3.	How to Detect Area of a Square?
iv.	FAQs on Area of a Square

What is the Expanse of Square?

A foursquare is a airtight 2-dimensional shape with four equal sides and four equal angles. The four sides of the square form the 4 angles at the vertices. The sum of the total length of the sides of a square is its perimeter, and the total space occupied by the shape is the surface area of the square. It is a quadrilateral with the following properties.

The opposite sides are parallel.
All four sides are equal.
All angles measure 90º.

Squares tin can be found all around united states of america. Here are some usually seen objects which take the shape of a square. The chessboard, the clock, a blackboard, a tile, are all examples of a square.

Expanse of a Foursquare Definition

The area of a foursquare is the measure of the space or surface occupied by it. It is equal to the product of the length of its two sides. Since the area of a square is the product of its 2 sides, the unit of the area is given in foursquare units.

Observe the below foursquare shown below. It has occupied 25 squares. Therefore, the area of the square is 25 square units. From the figure, we tin detect that the length of each side is five units. Therefore, the area of the square is the product of its sides. Area of foursquare = side × side = five × five = 25 square units.

Example of Area of a Square

Square Definition

A square is a two-dimensional shape quadrilateral with four sides equal and parallel to each other. The angles in this shape are measured equally 90 degrees.

Area of a Square Formula

The formula for the area of a foursquare when the sides are given is:

Area of a square = Side × Side = Sⁱⁱ

Algebraically, the surface area of a square tin can be found by squaring the number representing the measure of the side of the square. Now, let us use this formula to find the surface area of a square of side 7 cm. We know that the area of a square = Side × Side. Substituting the length of side every bit vii cm, 7 × 7 = 49. Therefore, the expanse of the given foursquare is 49 cm².

The area of a square can also be constitute with the assist of the diagonal of the foursquare. The formula used to find the area of a square when the diagonal is given is:

Surface area of a foursquare using diagonals = Diagonal²/two.

Allow us sympathize the derivation of this formula with the help of the post-obit figure, where 'd' is the diagonal and 'south' represents the sides of the square.

Hither the side of the square is 'due south' and the diagonal of the foursquare is 'd'. Applying the Pythagoras theorem nosotros take d² = south² + s²; d² = 2sⁱⁱ; d = √2s; s = d/√2. Now, this formula will help usa to find the area of the square, using the diagonal. Area = southward² = (d/√ii)^two = dⁱⁱ/2. Therefore, the area of the foursquare is equal to d^two/2.

Area of a Square

How to Discover Expanse of a Square?

In the in a higher place section, we covered the definition of area of foursquare as well as area of foursquare formula. In this section let us understand how to use the area of the foursquare formula to discover its area with the help of few applications or real-world examples.

Area of Square When the Perimeter of a Square is Given

Example: Detect the area of a foursquare park whose perimeter is 360 ft.

Solution:
Given: Perimeter of the square park = 360ft
We know that,
Perimeter of a square = four × side
⇒ iv × side = 360
⇒ side = 360/4
⇒ side = 90ft
Area of a square = sideⁱⁱ
Hence, Area of the foursquare park = 90² = 90 × ninety = 8100 ft²
Thus, the expanse of a square park whose perimeter is 360 ft is 8100 ft².

Area of Square When the Side of a Foursquare is Given

Example: Notice the area of a square park whose side is 90 ft.

Solution:
Given: Side of the square park = 90ft
We know that,
Area of a square = ftⁱⁱ
Hence, Area of the square park = 90^two = ninety × ninety = 8100 ft²
Thus, the area of a square park whose side is 90 ft is 8100 ft²

Area of Square When the Diagonal of a Square is Given

Instance: Observe the expanse of a square park whose diagonal is xiv feet.

Solution:
Given: Diagonal of the square park = 14 ft
We know that,
Expanse of a square formula when diagonal is given = d²/two
Hence, Expanse of the square park = (xiv × 14)/2 = 98 ft^two
Thus, the expanse of a square park whose diagonal is 14 m is 98 ft^two.

Surface area of Square Tips:

Note the post-obit points which should be remembered while nosotros summate the area of a square.

A common mistake that nosotros tend to make while computing the area of a square is doubling the number. This is incorrect! Ever remember that the area of a foursquare is side × side and not two × sides.
When we stand for the expanse, we should not forget to write its unit of measurement. The side of a square is i-dimensional and the area of a foursquare is ii-dimensional. Hence, the expanse of a square is e'er represented as foursquare units. For case, a foursquare with a side of 3 units will have an area of 3 × 3 = 9 square units.

☛ Related Manufactures

Diagonal of Square
Surface area of Squares and Rectangles Worksheets
Perimeter of Foursquare
Area of a Square Prism

Area of a Foursquare Examples

Example one: What is the area of a square-shaped swimming pool whose one side is equal to 8 m?

Solution:

We know that ane side of the swimming pool is eight grand, so, we will apply the formula: Expanse of a square = side × side = 8 × 8 = 64 m^two. Therefore, the area of the swimming puddle is 64 square meters.
Case 2: The expanse of a square-shaped carrom lath is 3600 cmⁱⁱ. What is the length of its side?

Solution:

Area of the foursquare carrom lath = 3600 cm^two. Nosotros know that Surface area = side × side = side². So, side = √Area = √3600 = 60 cm. Therefore, the side of the carrom board is 60 cm.
Example 3: Find the area of the square-shaped flooring room which is made upwards of 100 square tiles of side fifteen inches.

Solution:

Area of one tile = 15 inch × 15 inch= 225 foursquare inches. Nosotros know that in that location are 100 tiles on the floor of the room. Thus, the expanse occupied by 100 tiles is the floor surface area = 100 × 225 square inches = 22500 square inches. Therefore, the surface area of the floor is 22500 foursquare inches.
Example iv: Find the area of a square carpet whose diagonal is 4 feet.

Solution:

The surface area of a square when its diagonal is given is D²/2. Given, diagonal d = 4 ft. Area of the carpet = (four × 4)/ii = xvi/2 = 8 square anxiety. Therefore, the expanse of the carpet is eight square feet.

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FAQs on Surface area of Square

What is Area of Square in Geometry?

In geometry, the square is a shape with 4 equal sides. The surface area of a square is defined as the number of square units that make a complete square. It is calculated past using the area of square formula Area = s × s = sⁱⁱ in square units.

What is the Expanse of a Foursquare Formula?

When the side of a square is known, the formula used to find the area of a square with side 's': Area = south × s = sⁱⁱ. When the diagonal 'd' of the foursquare is given, and so the formula used to find the surface area is, Expanse = d²/2.

How Do You Calculate the Expanse of a Square?

The area of a foursquare is calculated with the help of the formula: Expanse = s × s, where, 's' is one side of the square. Since the area of a foursquare is a ii-dimensional quantity, it is always expressed in square units. For example, if we want to summate the area of a square with side 4 units, information technology will be: A = 4 × four = xvi unit of measurementⁱⁱ. Check now expanse of square computer for quick calculations.

What is the Perimeter and Area of Foursquare Formulas?

The perimeter of a square is a sum of four sides of a square that is P = 4 × Sides. It is given in terms of m, cm, ft, inches.
The expanse of square = Area = southward × s, where, 's' is one side of the foursquare. It is given in terms of 1000^two, cm², ftⁱⁱ, in².

Check:

Perimeter Formulas
Volume Formulas
Expanse Formulas
Measurement Formulas

How to Find the Expanse of a Square From the Diagonal of a Foursquare?

The area of a square can also exist constitute if the diagonal of a square is given. The formula that is used in this case is: Expanse of a square using diagonals = Diagonal²/2. For example, the diagonal of a square is vi units, the Expanse = 6²/2 = 36/two = xviii square units.

How to Find the Area of a Square From the Perimeter of the Square?

The area of a square can exist calculated if the perimeter of the foursquare is known. Since the perimeter of a foursquare is: P = 4 × side, we tin observe the side of the foursquare 's' = Perimeter/4. Subsequently getting the side, the expanse of a square can exist calculated with the formula: A = s × s. For instance, if the perimeter of a foursquare is 32 units, we will substitute this value in the formula: P = 4 × side. 32 = 4 × side. So, the side will be eight units. Now, we can calculate the area of the square with side 8 units. Expanse = due south × s = viii × 8 = 64 square units.

What are the Units of the Surface area of a Square?

Since the expanse of a square is a two-dimensional shape, it is e'er expressed in foursquare units The mutual units of the area of a foursquare are mⁱⁱ, inches², cm^two, foot^two.

What is the Area of a Square Inscribed In a Circumvolve?

If a square is inscribed in a circumvolve, the diagonal of the square is equal to the diameter of the circle. And so, if the bore of the circle is given, this value can exist used every bit the diagonal of the square, and the surface area of the square can exist calculated with the formula: Area of a square using diagonals = Diagonal²/2.