Question

In the given figure, ABCD is a rectangle with AB = 80 cm and BC = 70 cm, ∠AED = 90° and DE = 42 cm. A semicircle is drawn, taking BC as diameter. Find the area of the shaded region.

Answer 1

We know that the opposite sides of a rectangle are equal

AD = BC =  70 cm

In right triangle AED

AE² = AD² − DE²  
= (70)² − (42)² 
= 4900 − 1764

= 3136
∴ AE² = 3136
⇒ AE = 56
= 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]`

`= 80xx70-[1/2xx56xx42+1/2xx22/7(70/2)^2]`

= 5600 - 3101

= 2499 cm²

Hence, the area of shaded region is 2499 cm²