non parallel sides of an isosceles trapezium are produced an equilateral triangle with sides of 6 and should be formed knowing that the trapezium is half the height of the triangle calculate the area of the trapezium
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Answer:
R.E.F. Image.
we know attitude is also a median in an equilateral triangle.
Therefore, BG = GC = 3 cm.
From ΔABG by Pythagoras theorem.
(AB)
2
=(AG)
2
+(BG)
2
(6)
2
=(AG)
2
+(3)
2
(AG)=
36−9
AG=
27
=5.20cm.
Height of trapezium = 2.60 cm → (given in question ⇒
2
5.20
=2.60cm)
Parallel side of the trapezium: a=BC=6cmand b=DE=
2
BC
=
2
6
=3cm {∵ its an equilateral triangle}
Therefore, Area of trapezium =
2
(a+b)×h
=
2
(6+3)×2.60
=9×1.3=11.70cm
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