in an isosceles trapezium ABCD angle A =60 degree and ac=20 cm and ad= 15 cm find the length of a b
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8th
Maths
Mensuration
Area of Trapezium
In the adjoining figure, AB...
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Asked on December 26, 2019 by
Mani Lunagaria
In the adjoining figure, ABCD is an isosceles trapezium. If ∠A=60
o
,DC=20 cm and AD=15 cm, find the length of AB.
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ANSWER
In triangle ADM.
cos60
0
=
12
AM
AM=12cos60
0
=6cm
So by symmetry BN=6cm
Hence AB=AM+NM+NB=6+16+6=28cm
Now,
sin60
0
=
12
DM
2
3
=
12
DM
⇒DM=6
3
So are of trapezium =
2
1
×(AB+CD)×DM
=
2
1
(28+16)×6
3
=132
3
cm
2
≈16cm
We get,
length of AB=16cm
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