How to calculate the area of the shaded segment, giving answer to the nearest square centimetre?

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1 Answer
CW
Jan 26, 2018

area of shaded segment #=41 " cm"^2#

Explanation:

enter image source here
Area of minor sector #OAB : A_1=pir^2*(theta/360^@)=90#
#=> theta=(90xx360)/(pi*10^2)=103.1324^@#
Area of #DeltaOAB: A_2=1/2*r^2*sintheta#
#=1/2*10^2*sin103.1324~~48.69 " cm"^2#
Area of the shaded segment #=A_1-A_2=90-48.69~~41.31 " cm"^2=41 " cm"^2 " (to the nearest square centimeter)"#

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