Q. 15.0( 5 Votes )

A rectangle whose length and breadth are 12 cm and 5 cm respectively is inscribed in a circle. Find the area of the blue coloured region, as shown in the figure 13.19.



Figure 13.19

Answer :

given length (l) = 12 cm


breadth (b) = 5 cm


we can notice from the fig. that the Hypotenuse of ADB is same as diameter of the circle.


from the triangle ABD


BD2 = AD2 + AB2


BD = √(52 + 122)


( AD is breadth, AB is length of the rectangle)


BD = √(25 + 144)


= √169


= 13 cm


diameter of the circle = 13 cm


Radius of the circle (r) = 6.5 cm


Area of the shade region = Area of circle – area of rectangle


= π r2 – b × h


= π × 6.52 – 5 × 12


= 72.732 cm2


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