Question

Find the area of the shaded region in the figure If ABCD is a rectangle with sides 8 cm and 6 cm and O is the centre of the circle. (Take π= 3.14)

Answer 1

Here, diagonal AC also represents the diameter of the circle. 

Using Pythagoras theorem:

AC = `sqrt(AB^2 + BC^2)`

AC = `sqrt(8^2 + 6^2)`

AC = `sqrt(64 + 36)`

AC = `sqrt100`

AC = 10

RAdius of the circle, OC = `"AC"/2 = 5 "cm"` 

Area of the shaded region = Area of the circle - Area of rectangle

= `pi"r"^2 - "AB"xx"BC"`

= `pi ("OC")^2 - "AB"xx"BC"`

= 3.14 x 5² - 8 x 6

= 78.5 - 48

= 30.5

Therefore, the area of shaded region is 30.5 cm² .