Rectangle

A rectangle is a shape with four sides and four corners. The corners are all right angles. It follows that the lengths of the pairs of sides opposite each other must be equal.

People make many rectangular things, including most tables, boxes, books, and papers.

A rectangle with all four sides equal in length is called a square.

PROPERTIES OF RECTANGLE:

1. The opposite sides are equal.
2. All angles are equal.
3. Each angle is a right angle.
4. The diagonals are equal in length.
5. The diagonals bisect each other.

FORMULAS OF RECTANGLE:

 Area of Rectangle=length*breadth

                              =l*b sq.units.

Perimeter of Rectangle=2(l+b) units.

Square

A square is a shape with four equal sides and four corners that are all right angles (90 degrees). The diagonals of a square also cross at right angles. The angle between any diagonal and a side of a square is 45 degrees. A square has rotational symmetry of four. It has four lines of regular symmetry.

A square is a type of rectangle with all sides of equal length. However note that while a square is a type of rectangle, a rectangle does not necessarily need to be a square.

A square is also the 2-dimensional analogue of a cube.

PROPERTIES OF SQUARE:

1. All the angles are equal.                                                                    
2. All the sides are of equal length.
3. Each of the angle is a right angle.
4. The diagonal are of equal length and breadth.
5. The diagonals bisect each other at right angles.

FORMULAS:

  Area of square=side*side

                       A=a*a 

                         =a² sq.units

 Perimeter of square=4a units

Circle

A circle is a round, two-dimensional shape. All points on the edge of the circle are at the same distance from the centre.

The radius of a circle is a line from the centre of the circle to a point on the side. Mathematicians use the letter r for the length of a circle's radius. The centre of a circle is the point in the very middle.

The diameter (meaning "all the way across") of a circle is a straight line that goes from one side to the opposite and right through the centre of the circle. Mathematicians use the letter d for the length of this line. The diameter of a circle is equal to twice its radius (d equals 2 times r).

${\displaystyle d=2\ r}$

The circumference (meaning "all the way around") of a circle is the line that goes around the centre of the circle. Mathematicians use the letter C for the length of this line.

The number π (written as the Greek letter pi) is a very useful number. It is the length of the circumference divided by the length of the diameter (π equals C divided by d). As a fraction the number π is equal to about ²²⁄₇ or 335/113 (which is closer) and as a number it is about 3.1415926535.

	${\displaystyle \pi ={\frac {C}{d}}}$
${\displaystyle \therefore }$	${\displaystyle C=2\pi \,r}$

The area, a, inside a circle is equal to the radius multiplied by itself, then multiplied by π (a equals π times r times r).

${\displaystyle A=\pi \,r^{2}}$

Calculating π

π can be measured by drawing a large circle, then measuring its diameter (d) and circumference (C). This is because the circumference of a circle is always π times its diameter.

${\displaystyle \pi ={\frac {C}{d}}}$

π can also be calculated by only using mathematical methods. Most methods used for calculating the value of π have desirable mathematical properties. However, they are hard to understand without knowing trigonometry and calculus. However, some methods are quite simple, such as this form of the Gregory-Leibniz series:

${\displaystyle \pi ={\frac {4}{1}}-{\frac {4}{3}}+{\frac {4}{5}}-{\frac {4}{7}}+{\frac {4}{9}}-{\frac {4}{11}}\cdots }$

While that series is easy to write and calculate, it is not easy to see why it equals π. An easier to understand approach is to draw an imaginary circle of radius r centered at the origin. Then any point (x,y) whose distance d from the origin is less than r, calculated by the pythagorean theorem, will be inside the circle:

${\displaystyle d={\sqrt {x^{2}+y^{2}}}}$

Finding a set of points inside the circle allows the circle's area A to be estimated. For example, by using integer coordinates for a big r. Since the area A of a circle is π times the radius squared, π can be approximated by using:

${\displaystyle \pi ={\frac {A}{r^{2}}}}$

REFERENCE FROM WIKIPEDIA

Shapes

A shape is a geometric figure that can be described with mathematics. One way to classify shapes is to describe a bigger kind of shape that the shape is one of. For example, they can be classified by their different numbers of dimensions. Thus, circles are two-dimensional shapes so, like other 2D shapes, they will fit into a flat plane.

Three-dimensional objects like cubes will not fit inside a plane, because they are not flat. Four-dimensional shapes made of polygons are called polychorons, and shapes made of polygons of any dimension are polytopes.

Two shapes are said to be equal, if one can be changed into the other by turning, moving, growing, shrinking, or more than one of these in combination.

2D SHAPES:

• circles
• triangles
• ovals
• quadrilaterals
  • squares
  • rectangles
• octagons
• hexagons
• pentagons
• heptagon

These are two-dimensional shapes or flat plane geometry shapes. Their sides are made of straight or curved lines. They can have any number of sides. Plane figures made of lines are called polygons. Triangles and squares are examples of polygons.

3D SHAPES:

• spheres
• platonic solids
• cubes
• cones
• pyramids
• hemispheres
• cuboids
• cylinders
• prisms

These are three-dimensional shapes. Their sides are made of flat or curved surfaces.

REFERENCE FROM WIKIPEDIA