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Question
The parallel sides of a trapezium-shaped field are 25 m and 10 m and non-parallel sides are 14 m and 13 m. What is the area (in m2 ) of the field?
Options
204
196
156
144
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Solution
196
Explanation:
Height of the trapezium
AE = BF = h m
From Δ AED and Δ BCF,
(AE)2 = (BF)2
(14)2 - (15 - x)2 = (13)2 - x2
(196 - 169) = 225 - 30x
30x = 198
x = 6.6 m
In Δ BCF, (13)2 - (6.6)2 = h2
h = `sqrt(169 - 43.56)`
h = 11.2 m
Area of the trapezium
`= 1/2 xx ("a" + "b") xx "h"`
`= 1/2 (10 + 25) xx 11.2`
= 196 m2
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