The Area a(N) of a Square When You Know the Length N of a Side

Area of Square

The area of a square is defined as the number of square units needed to make full a square. In other words, when we want to find the area of a square, we consider the length of its side. Since all the sides of a square are equal, its area is the production of its two sides. The mutual units used to measure out the area of the square are foursquare meters, square feet, square inch, square cm.

The expanse of a foursquare can also be calculated with the help of other dimensions, such equally the diagonal and the perimeter of the square. Let us endeavor to understand more well-nigh the area of the square on this page.

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

What is the Expanse of Foursquare?

A square is a closed two-dimensional shape with four equal sides and four equal angles. The four sides of the square form the four 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 square is the surface area of the square. Information technology is a quadrilateral with the following backdrop.

  • The opposite sides are parallel.
  • All 4 sides are equal.
  • All angles measure 90º.

Squares can be establish all around us. Here are some commonly seen objects which have the shape of a square. The chessboard, the clock, a blackboard, a tile, are all examples of a square.

Definition of Area of a Square

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

Observe the green square shown below. Information technology has occupied 25 squares. Therefore, the expanse of the square is 25 square units. From the figure, we can find that the length of each side is 5 units. Therefore, the area of the square is the product of its sides. Area of square = side × side = 5 × 5 = 25 foursquare units.

Example of Area of a Square

Area of a Square Formula

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

Area of a square = Side × Side = S2

Algebraically, the area of a foursquare can be constitute by squaring the number representing the measure out of the side of the square. Now, let united states use this formula to observe the expanse of a square of side 7 cm. Nosotros know that the area of a square = Side × Side. Substituting the length of side vii cm, seven × 7 = 49. Therefore, the area of the given foursquare is 49 cmii.

The area of a square can also be found with the aid of the diagonal of the foursquare. The formula used to notice the area of a square when the diagonal is given is:

Area of a foursquare using diagonals = Diagonal2/2.

Let us sympathise the derivation of this formula with the help of the post-obit effigy, where 'd' is the diagonal and 's' represents the sides of the square.

Here the side of the foursquare is 'southward' and the diagonal of the square is 'd'. Applying the Pythagoras theorem we have d2 = due south2 + due south2; d2 = 2s2; d = √2s; southward = d/√2. Now, this formula will help us to find the area of the square, using the diagonal. Surface area = s2 = (d/√ii)2 = d2/2. Therefore, the surface area of the foursquare is equal to d2/2.

Area of a Square

How to Notice Area of a Square?

In the above section, we covered the definition of area of square too as expanse of square formula. In this section let the states understand how to apply the area of the foursquare formula to find its area with the help of few applications or real-earth examples.

Discover Surface area of Square When the Perimeter of a Square is Given

Example: Notice the area of a square park whose perimeter is 360 ft.
Solution:
Given: Perimeter of the square park = 360ft
Nosotros know that,
Perimeter of a foursquare = four × side
⇒ four × side = 360
⇒ side = 360/4
⇒ side = 90ft
Expanse of a square = side2
Hence, Expanse of the square park = 902 = 90 × 90 = 8100 ft2
Thus, the surface area of a square park whose perimeter is 360 ft is 8100 fttwo.

Find Area of Square When the Side of a Foursquare is Given

Instance: Find the surface area of a square park whose side is 90 ft.
Solution:
Given: Side of the square park = 90ft
We know that,
Surface area of a square = ft2
Hence, Area of the square park = 902 = ninety × 90 = 8100 ftii
Thus, the area of a square park whose side is 90 ft is 8100 ft2

Find Area of Square When the Diagonal of a Square is Given

Instance: Detect the area of a square park whose diagonal is xiv anxiety.
Solution:
Given: Diagonal of the foursquare park = 14 ft
We know that,
Area of a square formula when diagonal is given = d2/2
Hence, Area of the foursquare park = (14 × 14)/2 = 98 fttwo
Thus, the area of a square park whose diagonal is 14 yard is 98 fttwo.

Area of Square Tips:

Note the following points which should be remembered while we calculate the area of a square.

  • A mutual mistake that we tend to make while calculating the area of a square is doubling the number. This is incorrect! Ever remember that the surface area of a foursquare is side × side and non 2 × sides.

  • When we represent the area, we should not forget to write its unit. The side of a square is 1-dimensional and the surface area of a foursquare is 2-dimensional. Hence, the surface area of a square is always represented equally square units. For example, a square with a side of 3 units volition have an area of 3 × 3 = 9 foursquare units.

☛ Related Articles

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

FAQs on Surface area of Square

What is Surface area of Square in Geometry?

In geometry, the square is a shape with four equal sides. The expanse of a square is divers as the number of foursquare units that make a complete foursquare. Information technology is calculated by using the area of square formula Surface area = s × s = s2 in square units.

What Is the Formula For Finding the Area of a Foursquare?

When the side of a foursquare is known, the formula used to observe the expanse of a square with side 'southward': Expanse = south × due south = south2. When the diagonal 'd' of the foursquare is given, then the formula used to find the area is, Expanse = d2/2.

How Practice You lot Calculate the Area of a Foursquare?

The area of a square is calculated with the help of the formula: Surface area = s × south, where, 's' is 1 side of the square. Since the expanse of a foursquare is a two-dimensional quantity, information technology is ever expressed in square units. For example, if we want to summate the area of a square with side 4 units, information technology volition be: A = iv × 4 = 16 unit2. Cheque now area of square calculator for quick calculations.

What is the Perimeter and Surface area of Square Formulas?

The perimeter of a square is a sum of four sides of a foursquare that is P = four × Sides. It is given in terms of thousand, cm, ft, inches.
The expanse of square = Area = s × s, where, 'due south' is one side of the square. It is given in terms of mii, cmii, fttwo, intwo.

Check:

  • Perimeter Formulas
  • Volume Formulas
  • Surface Surface area Formulas
  • Measurement Formulas

How to Detect the Area of a Square From the Diagonal of a Square?

The area of a foursquare can also be establish if the diagonal of the square is given. The formula that is used in this instance is: Surface area of a square using diagonals = Diagonal²/2. For example, the diagonal of a square is 6 units, the Expanse = half dozen²/two = 36/two = 18 square units.

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

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

What Are the Units of the Area of a Foursquare?

Since the area of a foursquare is a ii-dimensional shape, it is ever expressed in square units The common units of the surface area of a square are thousand2, inchesii, cm2, pesii.

What Is the Surface area of a Square Inscribed In a Circle?

If a foursquare is inscribed in a circle, the diagonal of the square is equal to the diameter of the circle. So, if the diameter of the circle is given, this value can exist used equally the diagonal of the square, and the area of the square can exist calculated with the formula: Area of a square using diagonals = Diagonal²/2.

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Source: https://www.cuemath.com/measurement/area-of-square/

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