ABCD is a field in the shape of a trapezium, `AD||BC,/_ABC=90^(@)` and `/_ADC=60^(@)`. For sectors are formed with centres A,B,C and D, as shown in the figure. The radius of each sector is 14 m. 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`.

Answer

(i) `616cm^(2)` (ii) `884m^(2)`

Explanation

Since `AD||BC` and `/_ABC=90^(@)`, so `/_BAD=90^(@)`
Also `/_ADC=60^(@)` (given)
`:./_BCD=360^(@)-(90^(@)+90^(@)+60^(@))=120^(@)`
(i) Total area of 4 sectors `={pixx(14)^(2)xx(90/360+90/360+120/360+60/360)}m^(2)`
`={22/7xx14xx14xx(1/4+1/4+1/3+16)}m^(2)`
`=(2xx28xx1)m^(2)=616m^(2)`
(ii) Area of remaining portion `=` ar(trapezium ABCD)`-`total area of 4 sectors
`=[{1/2(55+45)xx30-616]m^(2)`
`=(1500-616)m^(2)=884m^(2)`.