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Mathematics

A square is inscribed in a circle of radius 7 cm. Find the area of the square.

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Answer

Diagonal of the square = Diameter of the circle.

Radius of circle = 7 cm

Diameter of circle = 2 x 7 cm = 14 cm

Diagonal of square = 14 cm

Let s be the side of square.

A square is inscribed in a circle of radius 7 cm. Find the area of the square. Area and Perimeter of Plane Figures, Concise Mathematics Solutions ICSE Class 9.

By using the Pythagoras theorem,

Base2 + Height2 = Hypotenuse2

⇒ s2 + s2 = 142

⇒ 2s2 = 196

⇒ s2 = 1962\dfrac{196}{2}

⇒ s2 = 98 cm

⇒ s = 98\sqrt{98} cm

Area of square = Side2

= (98)2(\sqrt{98})^2 cm2

= 98 cm2

Hence, the area of the square is 98 cm2.

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