complete the quadrilateral

whereas normally e.g. a square is a kite (because it fulfills all of the properties), for this task it seems more interesting to insist on non-special cases of the various quadrilaterals
so, for this task:

• a parallelogram is not a rectangle or a square
• a kite is not a rhombus or an arrowhead
• a rhombus is not a square 
• a trapezium is not an isosceles trapezium 
• etc.

students must use the one given side as it is presented - you should not extend or shorten it

establishing that you have found the largest possible shape (in terms of area) is not that easy...

question 10 has an 'easy' answer that it is incorrect (with sides of length (root 5) and 2)!

many thanks to Fawn Nguyen for producing her own (neat and US-friendly) version of this task

see the related task from Math Pickle

my solutions have these areas
(questions 21, 22 and 24 have two congruent shapes that will work)