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Question
A circular field has a perimeter of 650 m. A square plot having its vertices on the circumference of the field is marked in the field. Calculate the area of the square plot.
Solution
We have a circular field in which a square field is marked.
Let the radius of the circle be r. We have,
Perimeter=`650`
`2pi r=650`
`= r=325/pi`
Use Pythagoras theorem to find the side of square as,
`AB=sqrt(r^2+r^2)`
`=325/pi sqrt2`
So area of the square plot,
`=(AB)^2`
`=(325/pi sqrt2)^2 m^2`
`=((325(7))/22 sqrt2)^2 m^2`
`= 21387 m^2`
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