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.

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Solution

In the given question, the square is inscribed in the circle.
Circumference of circle = 2πr
650 = 222/7r
r = (6507)/44
r = 103.409 m
As the diagonal of the square plot is the diameter of the circle.
hence, r × 2 = d
so, Diameter = 103.4092
Diameter of circle = 206.818 m = Diagonal of square plot
Now,
Area of the square plot = 1/2 × d²
= 1/2 × (206.818)²
= 1/2 × 42773.68
Area of the square plot = 21386.84 sq m

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