Perimeter and Area of Plane Figures - Perimeter and Area of Composite Figures
Perimeter and Area of Plane Figures - Perimeter and Area of Composite Figures
The figure shows an ancient coin which was once used in China. The coin is in the shape of a circle of radius \(3\) cm with a square of sides \(x\) cm removed from its centre. The area of each face of the coin is \(7\pi\) cm\(^2\).
- Form an equation in \(x\) and show that it reduces to \(2\pi - x^2=0\).
- Solve the equation \(2\pi - x^2=0\).
- Find the perimeter of the square.
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Answer:(i) \(2\pi-x^2=0\). (ii) Algebraic roots \(x=\pm\sqrt{2\pi}\); the length is \(x=\sqrt{2\pi}\approx2.51\) cm. (iii) \(4\sqrt{2\pi}\approx10.0\) cm.
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