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A circular field has perimeter 660 m. A plot in the shape of a square having its vertices on the circumference is marked in the field. Calculate the area of the square field.

Mensuration

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Answer

By formula,

Perimeter = 2πr

⇒2πr=660⇒πr=330⇒r=330π=330227⇒r=330×722⇒r=30×72⇒r=15×7=105 m.\Rightarrow 2πr = 660 \\[1em] \Rightarrow πr = 330 \\[1em] \Rightarrow r = \dfrac{330}{π} = \dfrac{330}{\dfrac{22}{7}} \\[1em] \Rightarrow r = \dfrac{330 \times 7}{22} \\[1em] \Rightarrow r = \dfrac{30 \times 7}{2} \\[1em] \Rightarrow r = 15 \times 7 = 105 \text{ m}.

A circular field has perimeter 660 m. A plot in the shape of a square having its vertices on the circumference is marked in the field. Calculate the area of the square field. Mensuration, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

From figure,

BD = BO + OD = r + r = 2r = 2 × 105 = 210 m.

Let O be the center of the circle and ABCD be square of side x metres.

Area of square = (side)2 = x2.

In right angle triangle BCD,

⇒ BD2 = BC2 + CD2

⇒ 2102 = x2 + x2

⇒ 2x2 = 44100

⇒ x2 = 441002\dfrac{44100}{2} = 22050 m2.

Hence, area of square = 22050 m2.

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