Refer to the attached image.
We have to find the area of the shaded region.
Area of shaded region = 2(Area of rectangle ABCD) +2(Area of semicircle with radius AO - Area of semicircle with radius BO)
Area of rectangle with length 'l' and width 'w' is given by [tex] "l \times w".[/tex]Now, area of rectangle ABCD = [tex] AC \times CD [/tex]
= [tex] 100 \times 10 [/tex]
= 1000 sq. meters (equation 1)
Area of semicircle with radius 'r' is given by [tex] \frac{\Pi r^{2}}{2} [/tex]
Therefore, Area of semicircle with radius AO - Area of semicircle with radius BO
( AO=AB+BO = 10+30 = 40 m and BO= 30 m)
= [tex] (\frac{\Pi (40)^{2}}{2}-\frac{\Pi (30)^{2}}{2}) [/tex]
=[tex] \frac{\Pi }{2}(40^{2}-30^{2}) [/tex]
[tex] =\frac{\Pi }{2}(700) [/tex] (equation 2)
Therefore,
Area of shaded region
= 2(1000) + 2([tex] \frac{\Pi }{2}(700) [/tex]) (from equations 1 and 2)
= (2000 + 700[tex] \Pi [/tex]) square meters.
