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Question
Length of the fence of a trapezium shaped field ABCD is 120 m. If BC = 48 m, CD = 17 m and AD = 40 m, find the area of this field. Side AB is perpendicular to the parallel sides AD and BC.
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Solution
AB = DE
EC = BC − BE
EC = (48 − 40) m
EC = 8 m
In Δ DEC,
(DE)2 + (EC)2 = (D C)2
(DE)2 + (8)2 = (17)2
(DE)2 = (17)2 − (8)2
DE = 289 − 64
DE = 225 m2
DE = `sqrt225` m
DE = 15 m
AB = 15 m
Area of trapezium, ABCD
`= 1/2` × (sum of parallel sides) × Height
`= 1/2` × (AD + BC) × AB
`1/2` × (40 + 48) ×15
= 660m2
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