Question

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.]

Answer 1

In right triangle AED

AD² = AE² + DE²  
= (9)² + (12)² 
= 81 + 144
= 225
∴ AD² = 225
⇒ AD = 15 cm
We know that the opposite sides of a rectangle are equal
AD = BC =  15 cm
= Area of the shaded region = Area of rectangle − Area of triangle  AED + Area of semicircle

`="AB"xx"BC" - 1/2xx"AE"xx"DE"+1/2pi("BC"/2)^2`

`= 20xx15-1/2xx9xx12+1/2xx3.14(15/2) `^2

=  300 -  54   + 88.31

= 334. 31 cm²

Hence, the area of shaded region is 334.31 cm²