Square

A closed figure is called a polygon; numerous shapes or polygons have different sides and angle ratios. The polygons with four sides give a class of shapes called quadrilaterals. There are various types of quadrilaterals with their different properties. This article will talk about the most basic type of quadrilateral – square. So, in this article, we will talk about this most basic quadrilateral –  square, covering its definition, square properties, square Area and perimeter of the square, and formulas for square Area and perimeter of the square. So stick with us till the last to know about Square.

Square

A square is a quadrilateral ( a polygon with four sides ) with all four sides equal in length, and all interior angles are equal and 90 degrees in measurement. The form of the square is such that if a plane is sliced through it from the centre, both parts are symmetrical. Each half of the square now resembles a rectangle with equal sides.

A square has four sides equal, but a rhombus also has four sides equal square has all angles equal, but this property is also possessed by another quadrilateral – rectangle. Then what makes the square unique is that all sides are equal, all angles of equal measurement, and the measurement of all the angles is fixed, that is 90 degrees. The diagonals of a square are equal and bisect each other at 90 degrees. These are also called square properties.

Examples Of Square

Following are some examples of squares:

• Floor and Wall Tiles.
• Paper Napkins.
• Chess Board.
• Cushions.
• Bread

Square properties

The following are the most important square properties or qualities of a square:

• Each of the four internal angles is 90 degrees.
• The square’s four sides are congruent or equivalent to one another.
• The square’s opposite sides are parallel to each other.
• The square’s diagonals are 90 degrees apart and bisect each other.
• The square’s two diagonals are equal to each other.
• The square has four vertices and four sides.
• The diagonal of the square divides it into two similar isosceles triangles
• The length of the diagonals is greater than the sides of the square

Square Area

In a two-dimensional plane, the Area of any shape is the Area or the space it covers. Generally, we have to find the Area of the square while calculating the square area parks. The Area is equal to the sides or side squared square in this case. A square unit is used to measure it.

square areas= side × side

If the length of a square’s side is ‘a,’ then Area = a2 sq. unit.

Perimeter

The perimeter is the length of the boundary. We calculate the perimeter while fencing and doing things related to the boundary. The square’s perimeter is equal to the sum of its four sides. The perimeter is measured in the same unit as the square’s side length.

Perimeter = side + side + side + side

The square’s perimeter equals four sides.

If the length of a square’s side is ‘a,’ then the perimeter is Perimeter = 4a unit.

Square’s Diagonal Length

The diagonal length of the square is equal to s, where s is the square’s side. The lengths of the diagonals are equal. Applying Pythagoras’ theorem, the diagonal is the hypotenuse in any square or rectangle. The perpendicular and base are the two sides of the triangle produced by the square’s diagonal.

Since, Base2 + Perpendicular2 = Hypotenuse2

Diagonal2 = Side2 + Side2 is the result.

d = s2 = diagonal

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

square’s diagonal

The square’s diagonal is a line segment that links the square’s two opposed vertices.

A square is a two-dimensional plane shape having four equal sides and all four angles equal to 90 degrees, according to geometry. The features of a rectangle are similar to those of a square. However, the distinction is that a rectangle only has equal opposite sides. As a result, a rectangle is only considered a square if all four sides have the same length. The perimeter, square area and square diagonal length are part of square properties.

Conclusion

We hope that now you are well familiar with the shape of the square and its properties. The formula for square perimeters and squares areas has applications in daily life, and also, questions are being asked on the same concept in many competitive exams. After reading this, you can attempt some exercises and tests to check your conceptual understanding.