## 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

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