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Rectangle

In the quadri...

Question

In the quadrilateral given below, $A B | | D C$ , $E$ and $F$ are mid point of of non-parallel sides $A D$ and $B C$ respectively. Calculate $A B$ , if $D C = 8 c m$ and $E F = 9 c m$ .

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Solution

It is given that
A Quadrilateral which AB||DC
E and F is the mid point of non-parallel sides AD and BC
To prove:
(i) EF , if AB=6 cm and DC=4 cm
(ii) AB , if DC=8 cm and EF=9 cm
Proof:
We know that
The length of the segment joining the mid point of two non-parallel sides is half sum of the lengths of the parallel sides
E and F are the midpoints of AD and BC,
EF=12(AB+CD).....(1)
AB=6 cm and DC=4 cm
Substituting in equation (1)
EF=182(6+4)
By further calculation
EF=12×10=5 cm
(ii) DC=8 cm and EF=9 cm
Substituting equation (1)
EF=12(AB+DC)
By further calculation 9=12(AB+8)
18=AB+8
So we get,
18−8=AB
AB=10 cm

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In the quadrilateral given below, AB||DC, E and F are mid point of of non-parallel sides AD and BC respectively. Calculate AB, if DC=8cm and EF=9cm.

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