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 on a later occasion I could only find 18...

calculating their areas could involve an introduction to the square root of 2

although the areas can be found by subtracting 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

(12 different areas for the 19 (or is it 18?) different isosceles trapeziums on this grid)

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