A circular field has a perimeter of $650 m$ . A plot in the shape of square having its vertices on the circumference is marked in the field. Calculate the area of the square plot.

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Solution

$2 π r = 650 \Rightarrow r = \frac{650}{2 π}$

Clearly each diagonal of the square is a diameter of the circle.

Area $= \frac{1}{2} d^{2} = \frac{1}{2} (2 r)^{2} = \frac{1}{2} (\frac{650}{π})^{2} = \frac{422500}{20} = 21, 125$ $m^{2}$

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A circular field has a perimeter of 650 m. A plot in the shape of square having its vertices on the circumference is marked in the field. Calculate the area of the square plot.

2πr=650⇒r=6502πClearly each diagonal of the square is a diameter of the circle.Area =12d2=12(2r)2=12(650π)2=42250020=21,125 m2

A circular field has a perimeter of $650 m$ . A plot in the shape of square having its vertices on the circumference is marked in the field. Calculate the area of the square plot.

$2 π r = 650 \Rightarrow r = \frac{650}{2 π}$

Clearly each diagonal of the square is a diameter of the circle.

Area $= \frac{1}{2} d^{2} = \frac{1}{2} (2 r)^{2} = \frac{1}{2} (\frac{650}{π})^{2} = \frac{422500}{20} = 21, 125$ $m^{2}$