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

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

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