areas of isosceles trapeziums

a search for all the possible isosceles trapeziums on a 5 by 5 grid
can involve being systematic
once upon a time I thought I'd found 19 of them...
but then on a later occasion I could only find 18...
(help would be much appreciated...)

calculating their areas could involve an introduction to the square root of 2
although the areas can be found by subtracting (triangles) from a surrounding rectangle (frame)

the area of the second shape could be obtained by cutting it up or subtraction from a 3 by 3 square

and this related to the area of a trapezium formula

some isosceles trapeziums are drawn
with their vertices on the dots

draw some more

find their areas










what are the 12 different areas for the 19 (or is it 18?) altogether different isosceles trapeziums on a 5 by 5 dot grid