SOLUTION: In the figure, OAB and OXY are sectors of a circle with centre O. What is the area of the shaded region AXYB. Figure: https://imgur.com/a/uOKno

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Question 1106476: In the figure, OAB and OXY are sectors of a circle with centre O. What is the area of the shaded region AXYB.
Figure: https://imgur.com/a/uOKno

Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

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= %28theta+%2Api+%29%2F360+%2A+r%5E2 (when theta is in degrees)
Area of sector OXY:
OXY=+%28150+%2Api+%29%2F360+%2A+%289cm%29%5E2
OXY=+%285+%2Api+%29%2F12%2A+81cm%5E2
OXY+=+33.75+%2Api%2Acm%5E2
Area of sector OAB:
OAB=+%28150+%2Api+%29%2F360+%2A+%287cm%29%5E2
OAB=+%285+%2Api+%29%2F12%2A+49cm%5E2
OAB+=+20.417+%2Api%2Acm%5E2

the area of the shaded region AXYB:
OXY+-OAB=33.75+%2Api%2Acm%5E2+-20.417+%2Api%2Acm%5E2+=13.33%2Api%2Acm%5E2

Answer by ikleyn(52794) About Me  (Show Source):