In the figure, O is the centre of a circle such that diameter AB=13cm and AC=12cm. BC is joined. Find the area of the shaded region. (Take π=3.14)

In ΔABC, Angle in a semicircle, ∠C=90°
Therefore, by Pythagoras theorem
BC² + AC² = AB²
BC² + 12² = 13²
BC² = 169 - 144 = 25
BC = 5
Area of shaded region = Area of semicircle - Area of triangle
= (1/2)πr² - (1/2)bh
= (1/2) × 3.14 × (13/2)² - (1/2) × 5 × 12
= 3.14 × 13 × 13 / 8 - 30
= 66.3325 -30
Area of shaded region= 36.3325 cm²