if the perimeter of circle is equal to that of square then what is area in ratio ?
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Given,
the perimeter of the circle is equal to that of the square.
P
circle
=P
square
Let r be the radius of the circle & a besides of square, then
2πr=4a
[
a
r
=
2π
4
=
π
2
]
Now
Area of square
Area of circle
=
a
2
πr
2
=π(
a
r
)
2
Using
a
r
=
π
2
, we get
A
square
A
circle
=π(
π
2
)
2
=
π
2
4
×π=
π
4
Hence the ratio of Area of a circle to that of a square is
π
4
.
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