The diameter for the smaller semicircle is #2r#, find the expression for the shaded area? Now let the diameter of the larger semicircle be 5 calculate the area of the shaded area?

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Answer 1 · 2018-06-08T20:23:49

#color(blue)("Area of shaded region of smaller semicircle"=((8r^2-75)pi)/8#

#color(blue)("Area of shaded region of larger semicircle"=25/8 "units"^2#

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#"Area of " Delta OAC=1/2(5/2)(5/2)=25/8#

#"Area of Quadrant " OAEC=(5)^2(pi/2)=(25pi)/2#

#"Area of segment" AEC =(25pi)/2-25/8=(75pi)/8#

#"Area of Semicircle" ABC = r^2pi#

Area of shaded region of smaller semicircle is:

#"Area "=r^2pi-(75pi)/8=((8r^2-75)pi)/8#

Area of shaded region of larger semicircle is area of triangle OAC:

#"Area" = 25/8 "units"^2#