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THE MAGIC OF NATURE POEM WRITTEN BY SAFALYA PAL

THE MAGIC OF NATURE THE MAGIC OF NATURE OUR WONDER DOES GROW THE SECRETS OF NATURE ARE NOT FOR THE HUMANS TO KNOW THE MAGIC OF NATURE IS FOR ALL TO SEE IT IS ALL AROUND YOU AND ALL AROUND ME THE BEUTIFUL SCENIC VIEW EVERYTHING SEEMS AWESOME AND NEW LOOKING AT THE AWESOME SIGHT YOU FEEL SO TRANQUIL AND DELIGHT THINK HOW THE LUSH FORESTS ALWAYS REMAIN GREEN THINK WHY THE WATER DOESN’T ACCOMPLISH THINK HOW THE NORTHERN LIGHTS ESTABLISH THINK FROM WHERE DO WE GET NATURAL THINGS WE GET ALL THESE FROM THE NATURE AND THOSE ARE POSSIBLE FOR NATURE’S MAGIC! THE NATURAL BEAUTY OF NATURE HAS SO MUCH TO SAY, THE BEAUTIFUL CROSSROADS AND LONG WAY, THE NATURE HAS ITS CHARM, KEEP IT SAFE AND DO NOT HARM, THE NATURE WILL KEEP US UNSAFE, IF WE DON'T KEEP IT SAFE!                                               - SAFALYA PAL
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Mensuration, NCERT NOTES, Class 6

 

Mensuration

Introduction to Mensuration

Mensuration

  • Mensuration is the branch of mathematics that deals with the measurement of length, area or volume of various geometric shapes.

Shapes

  • A shape is the form of an object.
  • Examples of two-dimensional shapes are square, rectangle and triangle, and of three-dimensional shapes are cube, cuboid and sphere.

Perimeter

Perimeter

  • Perimeter is the total length or total distance covered along the boundary of a closed shape.
           
  • Perimeter of a circle is also called as the circumference of the circle.
        

Perimeter of a Triangle

            
  • Perimeter of triangle = Sum of lengths of all sides = a + b + c.
  • If the given triangle is equilateral that is if all the sides are equal (a  = b = c), then its perimeter is equal to 3 × length of one side of the triangle.

Perimeter of a Rectangle

          
  • Perimeter of the rectangle = length ( l ) + length ( l ) + width (w) + width (w)
                                                = 2× [length ( l ) + width (w)]

Perimeter of a Square

         
  • Perimeter of square =  4 × length of a side = 4a 

Perimeter of a 'n' sided polygon

  • A polygon is a closed shape made up of line segments.
  • Perimeter of n sided polygon = n × length of one side.
  • Example: Length of each side of a hexagon is a cm, then:
    Perimeter of the hexagon = 6a cm

Perimeter of irregular shapes

  • Irregular shapes are the shapes which do not have all sides and angles equal.
  • The perimeter of irregular shapes is equal to total length covered by the shape.
    In the figure given below, perimeter is the sum of all sides.

Area

Area

  • Area is the total amount of surface enclosed by a closed figure.

Area of Square

  • Area of a square = Side × Side =Side2=a2, where a is the length of each side.

Area of Rectangle

  •  Area = length ( l ) × breadth ( b)

Area of a triangle

 
  • Area of triangle =12×base×height=12×b×h
 

Areas of different types of triangles

  • Consider an acute and an obtuse triangle.
    Area of each triangle =12×base×height=12×b×h

Visualisation of Area

  • In the given graph, if area of each small square is 1 cm2, then
    Area of rectangle =l×b=5×2=10 cm2
    Area of square =a×a=2×2=4 cm2

Area of irregular shapes

  • Area of an irregular figure can be calculated :
    Step 1: Divide the irregular shape into regular shapes that you can recognize (eg. triangles, rectangles, circles and squares)
    Step 2: Find the area of these individual shapes and add them. Sum will be the area of the irregular figure.
     
  • Example: Area of the given figure = Area of MNCB + Area of AMGH + Area of EFND 
                                                          = [ 5 × 9 + 4 × 2 + 3 × 3 ] cm2 
                                                          = [45 + 8 + 9 ] cm2 
                                                          =62 cm2
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