Perimeter; Area of Square - Perimeter and Area, Mathematics, CBSE Class 7 Video Lecture

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start with a square so square being one
of the simplest polygons let us see how
do we find the perimeter and area of a
square so we start with perimeter now as
I have said what is parameter it is
nothing but the total length of the
boundary so when you look at the square
which is the boundary obviously this the
lines marked by in black so these lines
represent the boundary of the square now
let us say that the length of each side
is L because in a square we know that
the length of all the sides are equal so
one side is L all the other sides would
also be L so as per what we had
discussed parameter is what is parameter
so parameter for any geometrical shape
is the total length of boundary so what
forms the boundary in a square the four
sides right so that means the sum of the
length of the four sides so L plus L
plus L plus L this would give you the
total perimeter of the square now L
added four times what does that mean so
if you add the same number multiple
number of times you can write it as 4
multiplied by L or you can say that
perimeter of a square is 4 L where L is
the length of the side so we conclude
perimeter of a square is equal to 4 into
side what about area of a square now
instead of finding out the boundary if
we want to find out the region enclosed
by the square so area of a square is
given by side x side that is length of
one side multiplied by length of one
more side so that's interesting now you
might ask that how is that I mean how do
we get that so let us see the square
that is given to us the length of
each side of the square is 10
centimeters okay so if one side is 10
that means all the sides would be 10
centimeters in length so this is the
given square now if I have to find the
area so I actually need to find out the
entire region that is this entire yellow
region which is enclosed within the
square so let us try to understand the
concept like this so let's say that this
square is actually made up of many such
lines like the length of each of this
line is 10 centimeters right so let us
assume that this is a line of length 10
centimeters
now when many such lines are stacked
over each other how many such lines
now you see we are just adding one one
lining of 10 centimeter length so what
does happening gradually we are getting
a rectangle now if we can keep adding
more such lines of length 10 centimeter
what do we get we finally get a square
but when do we get the square we get a
square then the length of this is also
the length of the height or the height
is also 10 centimeter so that means what
we are actually doing is we are kind of
multiplying this length which is a 10
centimeter how many times we are
multiplying it ten times because we want
this also to be 10 centimeter please
understand this what we actually did was
we started with one line of length 10
centimeters so that is the length of
this line and now what we do we keep
adding we keep adding more such lines
until when do we add this so we keep
adding more and more lines until the
height or until the breadth is also
equal to 10 centimeter that is until
this length is also equal to 10
centimeter so what are you actually
doing we are actually keep we are
continuing to add one more line so when
we first
the first line so let us understand it
like this so when we added the first
line if I ask you to find out the area
of this line so in this case this is
just one line right so you have just
multiplied ten into one because you just
have one line of length and centimeter
now the moment we added two lines so
what the what happened to the a light is
like ten multiplied by two because now
you have two lines now in a similar way
if you keep adding one more line it
becomes 10 into 3 then 10 into 4 10 into
5 into 6 10 7 and so on and gradually by
the time you actually reach here what
what happens it is actually 10 into 10
so that is you have actually multiplied
1 10 centimeter line how many times 10
times and when you have placed that one
10 centimeter line 10 times what
happened the entire area that is covered
by these two lines together becomes 10
into 10 that is the area of the square
so please understand this so this is how
we get this concept or this is how we
actually derive the formula for area of
a square so I hope the parameter
particles clear because there we were
only concerned about the boundary but in
this case we are concerned about the
total area that is enclosed inside the
square so you have to assume that the
square is actually made up of many lines
each lines length is 10 centimeters so
therefore we are basically multiplying
that one line to get a square so in that
way what would be the area of the square
the area of the square would be 10 into
10 that is 100 centimeter square so this
would be the area of this square so what
does the unit for area because in case
of area let's say this the length is 10
centimeter so we are multiplying
sentimental with ten centimeters
centimeter x centimeter
gives it centimeter square similarly
instead of centimeter if the lengths are
in meters then the area would be in
meter square so meter square or
centimeter square is the unit for area
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