Length of the Diagonal of an Isosceles Trapezium
An isosceles trapezium has one line of symmetry. We can use this to find the length of the diagonal.
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
\[DF= \sqrt{DF^2 +FB^2} =\sqrt{10^2+9^2} =13.45 cm\]