Square

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Square Meaning

In Geometry, a square is a two-dimensional two-dimensional figure with four equal sides and every one the four angles are adequate to 90 degrees. The properties of a rectangle are somewhat similar to a square, but the difference between the two is, a rectangle has only its opposite sides equal. Therefore, a rectangle can be said to be a square as long as all its four sides are of equal length.


The Square

  • Number of sides = 4

  • Number of vertices = 4

  • Area = Side * Side

  • Perimeter of square formula = 4(Side)

The different properties for the square like the area and the perimeter of square formulae also differ from that of the rectangle. Let’s learn in detail about what is a square and its different properties.


Definition

Square may be a regular quadrilateral, which has all the four sides of equal length and every one of the four angles also are equal. The angles of the square are at right-angle or 90-degrees. The diagonals for the square are equal and also they bisect each other at 90 degrees.

A square also can be defined as a rectangle where two opposite sides have equal length.

(Image to be added soon)

The above figure represents a square where all the edges are equal and every angle equals 90 degrees.

Just like a rectangle, we will also consider a rhombus (which is additionally a convex quadrilateral and has all four sides equal), to be a square, if it's a right vertex angle.

In the very same way, the parallelogram with all of its two adjacent and equal sides and one right vertex angle is a square.


Shape of Square

A square may be a four-sided polygon which has it’s all sides equally long and therefore the measure of the angles are 90 degrees. The shape of the square is like if it's cut by a plane from the middle, then both the halves are symmetrical. Each half the square then seems like a rectangle with opposite sides equal.


Properties of a Square

The very important properties of a square are mentioned below:

  • All four interior angles are equal to 90°

  • All four sides of the square are congruent or equal to each other

  • The opposite sides of the square are parallel to each other

  • The diagonals of the square bisect one another at 90°

  • The two diagonals of the square are adequate to one another

  • The square has 4 vertices and 4 sides

  • The diagonal for the square when divided, comes out as two similar isosceles triangles

  • The length of the diagonals is greater than that of the sides for the square


Area and Perimeter of Square Formula

The area and perimeter are two main properties that outline a square as a square. Let us learn them one by one:


Area

Area of the square is the region covered by it during a two-dimensional plane. The area here is adequate to the square of the edges or side squared. It is measured in square units.

Area = side2 per square unit

If ‘a’ is that the length of the side of the square, then;

Area = a2 sq.unit

Also, learn to seek out the Area of Square Using Diagonals.


Perimeter

The perimeter of the square is adequate to the sum of all its four sides. The unit of the perimeter remains the same as that of the side-length of the square.

Perimeter equals Side + Side + Side + Side equals 4 Side

Perimeter = 4 × side of the square 

If ‘a’ is that the length of the side of the square, then perimeter is:

Perimeter = 4a unit


Length of Diagonal of Square

The length for the diagonals of square equals to s√2, where s is the side for the square. As, the length for the diagonals is equal to one another, by Pythagoras theorem, we can say, the diagonal is the hypotenuse and the two sides of the triangle formed by the diagonal of the square, are perpendicular and base.

          Since, Hypotenuse2 = Base2 + Perpendicular2

          Hence, Diagonal2 = side2 + side2

          Diagonal = √2side2

         d = s√2

Where d is that the length of the diagonal of a square and s is that the side of the square.

FAQ (Frequently Asked Questions)

1. What is the formula of the perimeter of a square?

As all the sides of a square are equal, we only need one side to find its perimeter. The perimeter for the given square is written as a + a + a + a equals 4a units. Therefore, the formula for the perimeter of the square equals 4 × (length of any one of the sides).

2. What is the area of a square?

The area is measured in "square" units. The area of a figure is the number of squares required to hide it completely, like tiles on a floor. Area of a square = side times side. As all the sides for the square are the same, it can be simply the length for 1 side squared.

3. What are the properties of a square?

Properties

  • The diagonals of a square bisect one another and meet at 90°.

  • The diagonals of a square bisect its angles.

  • Opposite sides of a square are both parallel and equally long.

  • All of the four angles for the square are the same (each of them being 360°/4 equals 90°, which is a right angle).

  • All four sides of a square are equal

4. What is the diagonal of a square?

Diagonal of a square may be a line segment that connects two opposite vertices of the square. As we've four vertices of a square, thus we will have two diagonals within a square. Diagonals for the square are always greater than the sides.