find the area of the shaded region in figure , if BC=BD=8cm,AC=AD=15cm and O is the centre of the circle.

SInce AOB is the diameter,

So, Angle ACB= Angle ADB= 90^{o}

Ar.(ABC)= Ar.(ABD)= 1/2 * BC* AC [Since BC= BD and AC= AD]

Ar.(ABC)= Ar.(ABD)= 60cm^{2}

By pythagoras theorem,

AB^{2}= AC^{2}+ BC^{2}

AB^{2}= 15^{2}+ 8^{2}

AB= 17cm

Therefore radius= 17/2 cm.

Ar. of C(O,r)= 22/7 * 17/2*17/2

= 3179/14 cm^{2}

Ar. of the shaded region= Ar. of C(o,r)- Ar.(ABC)- Ar.(ABD)

= 3179/14- 60- 60

= 1499 /14 cm^{2}