Length of the fence of a trapezium shaped field ABCD is 120 m. If BC = 48 cm, CD = 17 m and AD = 40 m, find the area of this field. Side AB is perpendicular to the parallel sides AD and BC.

Solution

Length of the fence = Perimeter
∴ AB + BC + CD + DA = 120
or AB + 48 + 17 + 40 = 120
or AB + 105 = 120
or AB = 120 - 105 = 15 m
∵ Area of a trapezium = $space space 1 half cross times left square bracket Sum space of space parallel space sides right square bracket space cross times space Height$
= $1 half cross times left parenthesis AD plus BC right parenthesis cross times AB$
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= $44 space cross times space 15 space straight m squared space equals space 660 space straight m squared$