Examples: Area of Polygons and Quadrilaterals Video Lecture - CTET & State TET

hello friends this video on mensuration
part 7 is brought to you by exam for
calm no more fear from exam question
number three top surface of a raised
platform is in the shape of a regular
octagon as shown in the figure
find the area of the octagonal surface
so what is an octagon
so octagon is a polygon with eight sides
and the regular octagon means all the
eight sides are equal in length so this
is our regular octagon let's name it
let's call it a b c d e f g h so this is
a regular oven so how do we find out the
area of this regular octagon so for that
first let's do one thing let's again do
the same concept of triangulation so
let's draw B G let's also draw C F so
the moment we draw B G and C F what
happens we are able to divide this
octagon into three parts the central
part is a rectangle this part is a
trapezium this part again is a trapezium
so this is a trapezium this is also a
trapezium and this one is a rectangle so
now we have to find out the area of the
trapezium and the rectangle separately
and add them up so how do we find out
the area of trapezium a H G B so we know
that area of a trapezium is equal to
half into height which is height is what
4 meters in this case so half into
height into some of the Paragon sites
that is a H plus B G so this would be a
h plus B G so this is half into 4 into a
H so what what is a H so if you look at
this G F is given as 5 meters so this is
a regular octagon so all the sides
be five meters in length so therefore a
H would also be five meters in length
what would be B G B G is given as 11
meters so this would be 11 so this is
half into 4 into 16 so two twos are four
16 to 32 so 32 meter square is the area
of the trapezium the top trapezium now
in a similar way you can find out the
area of the trapezium c d e f so in this
case also it would be 1/2 into height so
height here also would be 4 meters
because this trapezium and this
trapezium they are exactly identical so
their areas would also be same so 1/2
into height into some of the parallel
sides which is again the same here 5
plus 11 so this is also equal to 32
meter square now let's find out the area
of the rectangle so area of the
rectangle bc f G that is equal to length
into breadth so what is the length of
the rectangle 11 meters this is the
length and this is the bridge so 11 into
5 which is equal to 55 meter square
therefore the total area that is the
total area of the octagon will be equal
to 32 plus 32 plus 55 which is equal to
119 meter square so this would be the
area of the octagonal surface question
number 4 misses cause she has a square
plot with the measurement as shown in
the figure okay she wants to construct
the house in the middle of the plot a
garden is developed around the house
find the total cost of developing a
garden around the house at the rate of
rupees 55 per meter square so this is
what the plot is this the total plot the
green region represents the garden area
and the central portion represents
the house so we have to find out the
total cost for the garden so in order to
find the total cost for the garden we
need to find out the total area of the
garden so only the green area we need to
find out so for that what we will do let
us first find out the area of the house
so area of the house would be the area
of this green rectangle right which is
equal to length into print so what is
the length so length would be this
length which is given as 20 meters so
this would be 20 into break this 15
meter so 20 into 15 which is equal to
300 meter square now let us try to find
out the total area of the plot so the
entire area of the plot the plot again
here is in the shape of a square so if
you see the plot the plot itself is a
square then each side of the square is
given as 25 meters so the total area of
the square would be n into n which is 25
into 25 that is 625 meter square so
therefore the area of the garden is
equal to the total area of the plot
minus the area of the house so 625 minus
300 which is 325 meter square so this
green area is 325 meter square now let
us try to find out the cost so we see
that cost of gardening 1 meter square is
rupees 55 because it is given rupees 55
per meter square so one meter squares
cost is 55 therefore cost of 325 meter
square would be rupees 55 into 325 which
is equal to rupees seventeen thousand
875 so this would be the total cost for
developing the garden
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