In the given figure, from a rectangular region ABCD with AB = 20 cm, a right triangle AED with AE = 9 cm and DE = 12 cm, is cut off. On the other end, taking BC as diameter, a semicircle is added on outside the region. Find the area of the shaded region.
[ Use π = 3.14]
AED is a right angle triangle
= 225 cm2
⇒ AD = 15 cm
Area of the rectangular region ABCD
= AB××AD=(20×15)=300 cm2
Area of ∆AED
= 12×AE×DE=(12×9×12) cm2=54 cm2
In a rectangle
AD = BC = 15 cm
Since, BC is the diameter of the circle, the radius of the circle = 15 cm
Area of the semi-circle =12×π×r2
Area of the shaded region = Area of the rectangle + Area of the semi-circle − Area of the triangle
=(300+88.3125−54)=334.3125 cm2 .