All Formula of Square
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.
FAQs on Square Formula
1. What is Rhombus?
Rhombus is a four-sided quadrilateral with all its four sides equal in lengths. Rhombus is also referred to as a slanting square. Opposite sides of a rhombus are parallel. The properties of square and rhombus are similar, the only distinguishing property is that square has all the angles equal to 900, and rhombus does not. Rhombus is also called an equilateral quadrilateral. Also called a diamond or a lozenge. Every rhombus is a parallelogram but the vice versa is not true.
Some of the important properties of a rhombus are as follows:
The diagonals of a rhombus bisect each other and are perpendicular(forms right angle).
Opposite angles of the rhombus are equal and a diagonal bisects the internal angles.
Adjacent sides are equal in lengths.
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2. What is the Perimeter of Rectangle?
Perimeter of Rectangle
A four-sided polygon having two dimensions i.e. length and breadth are called a rectangle. To calculate the perimeter of the rectangle we have to add all the four sides of the rectangle.
In a rectangle, the opposite sides of a rectangle are equal and so, the perimeter will be twice the width of the rectangle plus twice the height of the rectangle.
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Perimeter of rectangle formula = sum of all the four sides
= length + width + length + width
= 2 length + 2 width
Perimeter of rectangle formula = 2 × (length + width)
Perimeter of rectangle formula = 2 × (length + width) = 2( l + b ) |
3. What is the importance of squares?
The square is the very basic structural Quadrilateral. The Mathematical concepts used in squares can be extrapolated to the three-dimensional structure like cubes. A basic understanding of geometry and aesthetics requires a good knowledge of Squares. Students can from their childhood start to recognize the geometrical figures by comparing them with this basic quadrilateral having equal sides and diagonal. It also helps to make the derivation of other formulas in geometry by the method of pictorial representation.
4. What are other methods to find the area of a square?
If the sides of a square are unknown and we have the length of its diagonals then we can find the area of the square by using the below formula.
Area = ½ × square of diagonal. There are also various other formulas for the determination of the area of squares which requires the knowledge of calculus. It will be studied in the higher classes. So up to this class these two methods are sufficient for finding the area of squares. Students can also use the graph paper method to find the area by counting the total number of unit squares in a bigger square.
5. Do I need to remember all the formulas for squares?
As we know square is a very basic structure among the Quadrilaterals. If we understand the derivation of the formulas in the square then it will be helpful for the students in higher classes. Many of the advanced concepts will be using the formulas of squares for solving complex problems.
Hence the students should not only remember but should understand how the formulas are derived. However, students must focus on the concept which we have tried to explain through the explanation above. Understanding the concept will help students remember the formula always.
6. Where can I find all the geometry formulas?
The best place to get the formulas is where it is distributed in segments and classified. There are a lot of materials available online but the materials provided by Vedantu stands out. The material available on the Vedantu website is carefully curated by the most experienced teachers and mathematicians. These will not only help you memorize it but also correlate the different formulas so that you can build a strong foundation for advanced use. Any student can avail of the study materials free of cost by just registering yourself with some basic details.
7. Is square formulas important for competitive exams?
There has not been a single competitive exam in the last 10 years where you don't have any questions from square formulas. It is a very basic but important concept in geometry that largely is used in aptitude questions in competitive exams. So we suggest the students be very clear in the concepts of square formulas. The formulas are also important from the point of your daily life. Every type of construction activity requires the knowledge of squares, in detail.