right-angled trapeziums

students initially consider the value that 'c' should have for the area to be a maximum

they can then look at their three different area values

and possibly establish that the differences between the differences will always differ by 1

e.g. for 3 , 4 , 5

• smallest area = 13.5
• middle area = 16
• largest area = 17.5

17.5 - 16 = 1.5
16 - 13.5 = 2.5

the differences from the middle one are 1 apart

proving this relationship involves quadratic expansions