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  • In Figure, a square of diagonal 8 cm is inscribed in acircle. Find the area of the shaded region.

In Figure, a square of diagonal 8 cm is inscribed in acircle. Find the area of the shaded region.

Answers (1)

[18.24 cm2]

Solution

Area of square =(side)2 ,                             

Area of circle =\pi r^{2}

 

Diagonal of square = Diameter of circle = 8 cm

Using Pythagoras theorem in \triangleABC
   (AB)^{2}+(BC)^{2}=(8)^{2}\\ a^{2}+a^{2}=(8)^{2}\\ 2a^{2}=(8)^{2}\\ a^{2}=\frac{64}{2}\\ a=\sqrt{32}=4\sqrt{2}

Area of square ABCD =a2

                =4\sqrt{2}\\ =32 cm^{2}

Diameter of circle = 8 cm

Radius (r) =\frac{8}{2}=4cm

Area of circle = \pi r^{2}\\

        = 3.14 \times 4 \times 4=50.24 cm^{2}

Area of shaded region = Area of circle – Area of square

                                    =50.24 - 32

                                    =18.24 cm2

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