# In the picture below you will see a square inside a square............Can you find the area of the circle?

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In the picture below you will see a square inside a square.

The inside square is drawn from the midpoints of all the four sides of the square.

Inside this square there is a circle.

Can you find the area of the circle?

posted Sep 9, 2016

As by using Pythagoras theorem
The side of inner square comes √32 m
And therefore the diameter of the circle is √32 m
Now, Radius of the circle is √32/2
So, Area of the circle is= pai x (radius sqaure)= pai x (√32/2) x (√32/2)= pai x 8 = 25.12 (m square)

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Consider the top left triangle which is isosceles right triangle ( 4, 4 and the hypotenus).
For any isosceles right triangle, the sides are in the ratio of 1 : 1 : square root of 2, Therefore The hypotenuse will be 4 * square root of 2.
This hypotenuse is also side of the inner square. Thereby the radius of the circle will be half of 4*sq. root of 2.

Meaning Radius = 2*sq.root of 2.

Area of circle = 22/7 (pai) * (radius square)

= (22/7)*4*2 = 25.143 sq.m

the diameter of circle is equal to side of inside square....so the radius=diameter/2=4/2=2......so area will be 3.14x2x2=12.56

The square inside the outer one has its side = sqrt (4^2 + 4^2)
= 4×2^(1/2) by pythagoras theorem which is nothing but the diameter of the inner circle.
Therefore the area of circle = pi×((2×2^(1/2))^2) =8×pi m^2

As by using pythogoras theorm
The side of inner square comes 4√2 m
And therefore the diameter of circle is 4√2 m
Therefore
Radius equals 2√2 m and area of circle is π2√2*2√2 = 25.12 m^2

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