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Square Rectangle Triangle

Introduction:

  • In geometry, a polygon is a plane figure which is bounded by a closed path or closed circuit which is composed of  finite sequence of straight line segments
  • Square,rectangleand triangle are the types of polygons and the basic important shapes in geometry. In this article, we are going to discuss some basic informations and formulas for square rectangle and triangle.
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Square:


Properties:

  • The diagonals  of a square bisect each other
  • The diagonals of a square are perpendicular.
  • Opposite sides of a square are both parallel and equal.
  • The diagonals of a square are equal.

 

Formulas:

  • The area of square           = (a)2
  • The perimeter of square  = 4 *  a

        where a ---> side length

Example problems:

1) Find the area of the square with the side length of 12 cm.

     Solution:

                  Area of square   = ( a ) 2

                                                = (12)2

                                               = 12 * 12

                    Area of square = 144 cm2

2) Find the perimeter of the square with side length of 31 feet.

     Solution:

             Perimeter of square = 4 * a

                                                  = 4 * 31

                                                  = 124

             Perimeter of square = 124 feet.


Rectangle:


Properties:

  • A rectangle is a four-sided polygon.
  • The opposite sides are parallel and of equal length.
  • Opposite angles are equal to 90 degree.
  • Diagonals are equal and bisect each other.

 

Formulas:

  •  Area of rectangle          =  l * w
  •  Perimeter of rectangle = 2( l + w )

       Where, l is the length and b is the width.

Examples:

1) Find the perimeter of rectangle with the length and width are 9 cm and 5 cm.

     Solution:

                                   p = 2( l+ w )

                                      = 2 (9+5)

                                      = 2(14)

                                      = 28 cm

2) Find the area of rectangle given the length is 21 m and width is 13 m.

     Solution:   

      Area of a Rectangle = l * w

                                           = 21 * 13

                                           = 273 m2


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Triangle:


Properties:

  • Triangles are formed using straight line segments
  •  The line segments connect three points that are not in a straight line.
  •  If the all sides are equal, then the triangle is known as equilateral triangle.


Formulas:

  • Area of Triangle  =  ½ b h                                

                  b ---> base
                  h ---> vertical height

  • Perimeter of equilateral triangle = 3 * a


Example problems:

1) Find the area of a triangle through base of 21 m and a height of 7 m.

     Solution:   

          Area of a triangle = ½ b h

                                         = ½ (21) (7)

                                         = 73.5 m2   

2) Find the perimeter of equilateral triangle with the side length 9 cm

     Solution:

                                    p =3 * a

                                       = 3*9

                                       = 27 cm