Fig shows a sector of a circle, centre O containing an angle θ.

Find the perimeter and area of the shaded region.

find i) perimeter = r (tan θ + sec θ + πθ/180 – 1)

ii)Area = r2/2(tan θ – πθ /180)

i need fully solved ..........hurry please....

tan theta =ab/oa

rtan theta =ab

arc length= pi*r*theta/180

cos theta=r/ob

ob=r/cos theta

bc =rsec theta-r

=r(sec theta-1)

perimeter=r tan theta +rsec theta -r +pi r theta/180

=r(tan theta+sec theta+pi theta/180-1)

hence proved.......:-)))