13. The area of an isosceles trapezium is 168 sq metres. If the lengths of the parallel
sides are 36 m and 20 m respectively, find the lengths of the non-parallel sides
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Given:
- Area of an isosceles trapezium is 168m²
- Length of parallel sides are 36m and 20m respectively.
To Find:
- Length of the non-parallel sides.
Solution:
Let ABCD be the isosceles trapezium with AC=20m and CO= 36m.
The area of the figure, (36-20)/2= 16/2= 8 m.
ABCD is 168 sq m.
Draw Of and BE perpendicular to CO from the vertices A and 8.
The area of the figure = (48+00)xh/2 =
168 [h = AF = BE ], or
(20+36 )×h = 2×168 = 336, or
h= 336/56 = 6m.
Now ADF and BCE are congruent right angle triangle, whose altitude is 6 m and the base=
(36-20)/2= 16/2 = 8m
The equal sides of the isosceles trapezium is
the same as the hypotenuse of ADF and BCF, which is [6² + 8² ]½= [ 36+64 ]½= 100½= 10m.
Hence, the length of the non-parallel sides will be 10m
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