Drao a vertical line from to E and another from B to F.

\[ED=CF=x\]

and \[8 +2x=12\]

since \[AB=EF\]

. Hence \[x=2\]

.Now draw the right angled triangle DBF.

Then

\[DF= \sqrt{DF^2 +FB^2} =\sqrt{10^2+9^2} =13.45 cm\]

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An isosceles trapezium has one line of symmetry. We can use this to find the length of the diagonal.

Now draw the right angled triangle DBF.

Drao a vertical line from to E and another from B to F.

\[ED=CF=x\]

and \[8 +2x=12\]

since \[AB=EF\]

. Hence \[x=2\]

.Now draw the right angled triangle DBF.

Then

\[DF= \sqrt{DF^2 +FB^2} =\sqrt{10^2+9^2} =13.45 cm\]