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in Perimeter and Area of Plane Figures by (46.2k points)
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What is the area of the region of the circle which is situated outside the inscribed square of side x?

(a) (π - 2)x2

(b) (π - 2)x2/2

(c) 2(π - 2)x2

(d) (π - 2)x2/4

1 Answer

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Best answer

(b) 

Diameter of the circle = AC 

= diagonal of the square = \(\sqrt2x\) cm

∴ Radius of the circle = \(\frac{\sqrt2x}{2}\) cm = \(\frac{x}{\sqrt2}\) cm

Hence, area of the circle = π(\(\frac{x}{\sqrt2}\))2 cm2

\(\frac{πx^2}{2}\) cm2

Area of the square = x2

∴ Required area = \(\frac{πx^2}{2}\) - x\(\frac{x^2}{2}\) (π - 2) cm2.

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