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.
