Question 1106476

You can work out the Area of a Sector by comparing its angle to the angle of a full circle.

angle {{{150}}} is {{{2.4}}} of a full circle ({{{360}}})

you have two sectors: 
{{{OXY}}} with {{{r=9cm}}} and central angle {{{150}}}

and sector 
{{{OAB}}} with {{{r=7cm}}} and central angle {{{150}}}

Area of the sector= {{{(theta *pi )/360 * r^2}}}   (when theta is in degrees) 

Area of sector {{{OXY}}}:
 {{{OXY= (150 *pi )/360 * (9cm)^2}}}
{{{OXY= (5 *pi )/12* 81cm^2}}}
{{{OXY = 33.75 *pi*cm^2}}} 

Area of sector {{{OAB}}}:
 {{{OAB= (150 *pi )/360 * (7cm)^2}}}
{{{OAB= (5 *pi )/12* 49cm^2}}}
{{{OAB = 20.417 *pi*cm^2}}}


the area of the shaded region AXYB:
 {{{OXY -OAB=33.75 *pi*cm^2 -20.417 *pi*cm^2 =13.33*pi*cm^2}}}