[Maths Class Notes] on Square Pdf for Exam

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

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 a square is 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 its 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 important properties of a square are mentioned below:

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 a Square

The length for the diagonals of the 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.

Below are some Amazing Facts about a Square :

• A square has 4 lines of reflectional symmetry, two lines on midpoints and two through the opposite vertices. 

• It’s all sides are congruent and all angles equal to 90 degrees. 

• If the perimeter is kept the same for all the quadrilaterals, the square has the largest area in all of them.

• The square can be defined as a specialized case of a rectangle, but the rectangle can not be defined in terms of a square.

The 3-D View of a Square : Cube

The square is a 2 dimensional shape whereas the cube has a three-dimensional solid shape. The cube has 6 faces, 12 edges, and 8 vertices. Also, the cube has all faces equal to the squares of the same length of side. Following are the points about a cube 

It’s volume is calculated by (side)³. Here, sides mainly consist of length, breadth, height. The volume here is in cubic units.

When a cube is opened, it gives 6 squares. 4 faces for the 4 sides , one for top and the last for bottom.

Examples of objects that are cube shaped include building, dice, box etc.