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Question
The area of a trapezium with equal non-parallel sides is 168 m2. If the lengths of the parallel sides are 36 m and 20 m, find the length of the non-parallel sides.
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Solution
Length of the parallel sides are 36 m and 20 m.
Area of a trapezium = 168 m2
∵ Area of a trapezium = `1/2 xx ["Sum af parallel sides"] xx "Height"`
∴ `168 = 1/2 xx [36 + 20] xx "Height"`
⇒ Height = `(168 xx 2)/56 = 336/56` = 6 m
In ΔACB, using Pythagoras theorem,
(AB)2 = (BC)2 + (AC)2
⇒ (AB)2 = (8)2 + (6)2
⇒ (AB)2 = 64 + 36
⇒ (AB)2 = 100
∴ AB = `sqrt(100)` = 10 m
Hence, length of the non-parallel side is 10 m.
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