Area and Perimeter

    Area and perimeter

What is measurement?

     The branch of mathematics which deals with the measure of length, angles, areas, perimeter in plane figures and surface area ,volumes in solid figures is called ‘measurement and mensuration’.

Measurement:

·    Measuring is a skill. It is required for every individual in his/her life.

·    Everyone of us has to measure something or the other in our daily life.

·    For example

Ø   The length of a rope required for drawing water from the well.

Ø   The length of the curtain cloth required for our door and windows.

What is area?

·    The mathematical term area can be defined as the amount of two-dimensional space taken up by an object.

·    The use of area has many practical applications in building, farming, architecture, science, and even deciding how much paint your bedroom.

What is perimeter?

·    The world perimeter means a path that surrounds an area.  It comes from Greek word ‘peri’, meaning around, and ‘metron’, which means measure.

·    The perimeter refers to the total length of the sides or edges of a polygon a two dimensional figure with angles.

·    The measurement around the circle we use the world circumference, which is simply the perimeter of a circle.

Definitions:

 Circle:

·    A 2-dimensional shape made by drawing a curve that is always the same distance from a centre.

 Semicircle:

·    A closed shape consisting of half a circle and a diameter of that circle.

·    A semicircle is a half circle formed by cutting a whole circle along a diameter line.

·    Any diameter of a circle cuts it into two equal semi circles

 Quadrant of a circle:

·    Cut the circle through two of its perpendicular diameters.

·    We get four equal parts of a circle. Each part is called quadrant of circle.

Formulae:

  Circle:

·    Area of the circle,

A=πr² sq. units.

·    Perimeter or circumference of a circle,

           P=2 πr units.

Where π ~ 22/7 or 3.14  

 Semicircle:

·    Area of the semi circle

           A=1/2*(area of the circle)

            =1/2* πr²

        A= πr²/2 sq. units.

·    Perimeter of  the semi circle

                P=1/2*(circumference of the circle)+2*r units 

                =1/2*2 πr+2r

             P= πr+2r

             P=( π+2)r units.

 Quadrant:

·    Area of a quadrant

Area, A=1/4*(area of the circle)

         A=1/4* πr² sq. units.

·    Perimeter of a quadrant

Perimeter, P=1/4*(circumference of

                             a circle)+2r units

                    =1/4*2πr+2r

                    =πr/2+2r

                P=( π/2+2)r units.

Applications:

     Find the perimeter of the semi circle whose radius is 14 cm.

Solution:

 Radius of a semi circle, r=14 cm

Perimeter of a semi circle,P=(π+2)r

                                                           units

                P=(22/7+2)*14

                  =(22+14/7)*14

                 =36/7*14

               =72 cm.

     Perimeter of a semi circle=72 cm.

Application of measurements:

Weather forecast:

Before leaving the house, we may want to check the weather. The temperature measured using thermometer will help us to determine what we choose to wear to keep us warm or cool.

 Cooking:

In cooking, we use measurements for volume when following recipe books. Tools such as measuring jugs may be used to determine volume.

 Trip:

When planning a car journey we may look at a map to find out the quickest way to reach a particular destination. The map allows us to compare the different distances. The time we take to travel can now be calculated by dividing distance over the speed of our car.

Applications in daily uses:

• — Amount of paint required to cover a certain surface area.
• — Amount of carpet required for a particular room.
• — Fencing needed for the perimeter of a garden.
• —The distance around a circular race track.
• — Gift wrapping.