ABCD is a field in the shape of a trapezium, `AD ||BC`, `angleABC=90^@` and `angleADC=60^@`, Four sectors are formed with centres A, B,C and D, as shown in the figure. The radius of each sector is 14m. Find the following: (i) total area of the four sectors, (ii) area of the remaining portion, given that `AD=55m, BC=45m` and `AB=30m`

Explanation

1)Total area of four sector`=pi/2*r^2/2+(pir^2)/4+(2pi)/3*1/2*r^2+pi/3*1/2*r^2`

`(pir^2)/2(1/2+1/2+2/3+1/3)`

`(pir^2)/22((3+3+4+2)/6)`

`((pir^2)/2)*2=pir^2`

`r=616m^2`

2)Area of trapezium`=1/2(a+b)*h`

`1/2*(45+55)*30=1500m^2`

Area of remaining portion`=1500-616=854m^2`.