Answer:
4.56
Step-by-step explanation:
i see a sector hosting 2 semi circles.
this sector area will be .25 of area of circle with radius 4ft.
area of sector = .25*π*16= 4π ft^2
area of semi circle of radius 2ft = .5π*4= 2πft^2
area of 2 semicircles = 4π
the total area of sector = area of 2 semicircles - intersection area + area not covered by semi circles
4π = 4π - intersection area+area not covered by semi circles
intersection area = area not covered by semi circles
now draw a square starting from the intersection point of 2 semi circles at their upper portion. the side will be 2ft
the area of intersection will be covered in the square.
area of intersection = 2*quarter area of circle of radius 2ft - area of square
= 2*(.25π4) - 4
2π-4 = 2.28
area of intersection = area not covered by semicircle
so area of shaded region = 4.56
