[Maths Class Notes] on Square Formula Pdf for Exam

Plane geometry or two-dimensional geometry deals with the flat figures that can be drawn on a piece of paper like lines, curves, polygons, quadrilaterals, etc.

A plane object that has only length and breadth is a 2-dimensional shape. Straight or curved lines make up the sides of this shape. Also, these figures can have any number of sides. A two-dimensional closed figure bounded with three or more than three straight lines is called a polygon. Triangles, squares, rectangles, pentagons, hexagons, are some examples of polygons.

For example, triangles and squares are polygons.

In this article let us study the square and all formulas of the square.

Square Formulas:

In Euclidean geometry, a polygon is a closed two-dimensional structure that has more than two sides where no two sides cross each other. Some of the basic polygons are Triangle, Quadrilateral and Pentagon. 

Square is one of the basic Quadrilaterals (which have four sides) with some definite structure. A Quadrilateral is said to be square when all the sides are of the same size and all the angles are equal. As the sum of all the angles is 360° in a Quadrilateral and all the angles are equal, each angle is 90° for any Square.

The opposite sides of the Square are parallel to each other. For this reason, the Squares are also called Parallelograms. The adjacent sides of the Square are perpendicular to each other for which all the squares are categorized as rectangles also.

There are many formulas associated with Square, so let us have a look at those.

The Perimeter of Square:

As all the sides of the square are equal (say s) the perimeter is four times the length of the side which is denoted by 4×s.

Area of Square:

Area of Square is the product of two sides(say s) which is denoted by s×s=s^2.

Diagonals of square: 

Both diagonals of the square are of the same length. They intersect each other at a right angle and each diagonal divides the square into two equal parts.

The length of diagonal “d” in square of side “s” can be found by using Pythagoras theorem.

[d^2=s^2+s^2]

 

=> [d^2=sqrt s^2+s^2]

 

=> [d=sqrt 2s^2]

 

=> [d=sqrt 2s]

From the above formula, we can see that the length of diagonals of squares is always greater than that of their sides.

Some Facts:

Among the Quadrilaterals, with the same perimeter, the squares have maximum area. 

For this reason, the square as a shape is used for engineering and architectural design for the planning of large buildings and cities.