29. The area of a trapezium with equal non-parallel sides is 168 m². If the lengths of
the parallel sides are 36m and 20m,find the length of each non-parallel side.
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Given :-
- Area of the trapezium = 168 m²
- Length of one parallel side = a = 36 m
- Length of other parallel side = b = 20 m
To Find :-
- Length of each non - parallel sides.
Solution :-
Draw perpendicular lines AE ⊥ FC and BD ⊥ FC.
We know that,
Putting the values together,
∴ Height of the trapezium = 6 m.
→ AE = BD
Now,
➲ AB = ED = 20 m.
➲ FC = AE = 36 m.
➲ FE = DC = ?
Value of FE :-
Therefore, FE = DC = 8.
Now,
We have to find the length of the non parallel sides.
According to the Question :-
Δ AEF is a right angled triangle.
By Pythagoras theorem :-
Length of one parallel side of the trapezium, AF = 10 m.
∴ AF = BC
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