ABCD is a field in the shape of a trapezium. AB||DC and ∠ABC=90∘,∠DAB=60∘. Four sectors are formed with centers A, B, C and D. The radius of Each sector is 17.5m. Find the
i). Total area of the four Sectors.
ii). Area of remaining portion given that AB=75 m and CD =50m.
Since AB||CD and ∠ABC=90∘. Therefore ∠BCD=90∘.
i) We have,
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.
ii) Let DL be perpendicular drawn from D on AB. Then,
AL= AB-BL=AB-CD =(75-50)m = 25m
In ΔALD, we have
Therefore area of trapezium ABCD =12 (AB+CD)DL
Area of the remaining portion = Area of trapezium ABCD - Area of 4 sectors
= 2706.25 – 962.5 = 1743.75 m2