In figure, arcs have been drawn of radius 21cm each with vertices A,B,C and D of quadrilateral ABCD as centres . Find the area of the shaded region.

Explanation

Specification of quadrilateral are not given, so quadrilateral may be of any shape.
As the radius of all 4 arcs are same equal to r = 21 cm but of different angles `angleA, angleB, angleC and angleD`.
So, there are four sectors of `angleA, anlgeB, angleC and angleD` with r = 21 cm
`:.` Area of shaded region `= (pi r_(1)^(2) (theta_(1)))/(360^(@)) + (pi r_(2)^(2) (theta_(2)))/(360^(@)) + (pi r_(3)^(2) (theta_(3)))/(360^(@)) + (pi r_(4)^(2) (theta_(4)))/(360^(@))`
`:' r_(1) = r_(2) = r_(3) - r_(4) = r` and
`angle theta_(1) + angle theta_(2) + angletheta_(3) + angle theta_(4) = 360^(@)` (interior `anlge s` of a quad)
So, area of shaded region
`= (pi r_(2) (theta_(1)))/(360^(@)) + (pi r^(2) (theta_(2)))/(360^(@)) + (pi r^(2) (theta_(3)))/(360^(@)) + (pi r^(2) (theta_(4)))/(360^(@))`
`= (pi r^(2))/(360^(@)) (theta_(1) + theta_(2) + theta_(3) + theta_(4))`
`= (pi r^(2))/(360^(@)) (360^(@))`
`= pi r^(2) = (22)/(7) xx 21 xx 21 = 22 xx 63 = 1386 cm^(2)`
Hence, the area of shaded region `= 1386 cm^(2)`