ABCD is a field in the shape of a trapezium. `AB || DC` and `/_A B C=90^@,` `/_D A B=60^@`. Four sectors are formed with centres `A ,B ,C` and `D`. The radius of each sector is 17.5 m. Find the total area of the four sectors.

Explanation

Since AB∣∣CD and `/_ ABC = 90^@`. Therefore `/_BCD = 90^@`.

Also, `/_DAB = 60^@`

∴`/_CDA=180^@−60^@=120^@`

Total area of the four sectors

= Area of sector at A + Area of sector at B + Area of sector at C + Area of sector at D

=`60^@/360^@ pi ×(17.5)^2+90^@/360^@ pi ×(17.5)^2+90^@/360^@ pi ×(17.5)^2+120^@/360^@ pi ×(17.5)^2`

=`{(1/6+1/4​+1/4​+1/3​)×pi×(17.5)^2}m^2`

= `962.5 m^2`