Question

Find the Area of Shaded Region bounded between two semicircles drawn on side of length 28cm of a rectangle as diameter. The other side of the rectangle is 14 cm long. Semi-Circles Rectangle Shaded Area

Answer 1

area of sector=`theta/360^o*pir^2=1/6pir^2`
area of segment(1)= area of sector - area of triangle
(1)=`(pir^2)/6+(pir^2)/6+sqrt3/4r^2`
(1)=`(pir^2)/3-sqrt3/4r^2`
`(1)+(2)=1/4pir^2`
`(2)=(pir^2)/4-(pir^2)/3+sqrt3/4r^2`
`(2)=sqrt3/4r^2-(pir^2)/12`
`(1)+(2)+(2)+(3)=r^2`
`(3)=r^2-1/4pir^2-sqrt3/4r^2+(pir^2)/12`
`(3)=r^2(1-sqrt3/4-pi/6)`
shaded region
=`2r^2(0.044)`
=`2(14)^2`(o.044)
=`17.248cm^2`