Question

in the figure AOB is a sector of angle 60° of a circle with centre O and radius 15cm if AP is perpendicular to OB and AP =12 find the area of shaded region​

Answer 1

Given :- 1) AP prependicular to AB

2) angle AOB or AoP = 60

Find :-area of shaded region

proof :- in trianglr Aop

• oa2=op2+ap2 (by pythogarous )
• therefore (15)2=op2+(12)2
• 225=op2+144
• 225-144=op2
• 81=op2
• under root81=op
• 9=op

area of triangle AOP=1/2*b*h

=1/2*9*12

=9*6

=54cm2

area of sector=angle/360*pie*radius2

=60/360*22/7*15*15

=1/6*22/7*15*15

=1/2*22/7*5*15

=11/7*75

= 825/7cm2

area of shaded region= area of sector -area of triangle

= 825/7-54cm2

=825-54*7/7

=825-378/7

answer =447/7 cm2