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A circular field has a perimeter of 660 m. A plot in the shape of a square having its vertices on the

the circumference is marked in the field. Calculate the area of the square field.

Answer:

It is given that

The perimeter of circular field = 660 m

The radius of the field = 660/2 π

Substituting the values

= (660 × 7)/ (2 × 22)

= 105 m

Here

ABCD is a square which is inscribed in the circle where AC is the diagonal which is the diameter of the circular

field

Consider a as the side of the square

AC = √2 a

a = AC/√2

Substituting the values

a = (105 × 2)/ √2

Multiply and divide by √2

a = (105 × 2 × √2)/ (√2 × √2)

By further calculation

a = (105 × 2 × √2)/ 2

a = 105 √2 m

We know that

\text { Area of the square }=\mathrm{a}^{2}

\begin{aligned} &\text { It can be written as }\\ &=(105 \sqrt{2})^{2}\\ &=105 \sqrt{2} \times 105 \sqrt{2}\\ &=22050 \mathrm{m}^{2} \end{aligned}

"hello and welcome my dear students
i am surprised the maths would run
leader and i am here
with a new question it is a circular
field as a perimeter of 660 meter
a plot in the shape of a square
having its vertices on this
circumference is marked in the
field calculate the area of the square
field
so without wasting much time let's have
a look at the solution
and before that we look at the important
points of this
question so the we know that a circular
field has a perimeter of
660 meters
so the perimeter is 660
meters also we observe that our plot is
in the shape of a square
having its vertices on the circumference
so let's look at the solution
so we have been given that perimeter
i'm writing p for perimeter
it's nothing but a 660 meter
and we know that the perimeter of a
circle is nothing but 2 pi
r which is equal to 660 meter
which further implies that r is nothing
but
equal to 660 by 2 pi
so further solving it we get
660 into 7 upon 2 into 22
you put the value of the pi which is 22
by 7
we get 105 meter
also we observe that if it is a square
which is inscribed
in the circle where ac is the diagonal
which is the diameter of the circular
field
circular field so i've written sirc
that means circular field let's consider
the side of square ba
so let's decide
of square
ba so we know that ac is nothing but
equals to root 2a
using the pythagoras theorem we know
that both the sides of the square are
equal
we get a diagonal as root 2 into a
which further implies that the side that
is a
is equals to ac by root 2.
so we'll substitute the values so we get
a as
105 into 2
by root 2
because 105
is the radius and ac is the diameter of
the circle
so by further calculation we get
105 into 2 into root 2
upon 2
which further implies that a is equals
to
105 root 2.
now the area of square is equals to
side square this we all know
and side is nothing but a square so
we'll simply
substitute the value so we get 105
root 2 square which is nothing but
equals to
22 50
meter square that is double two zero
five zero
meter square so i hope my students got
this question well
do not forget to hit the subscribe
button you can also share your doubts in
the comment section
see you next time bye"

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