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

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