It seems people are getting this whole question twisted up and going about it in a really complicated matter.
Let's clarify, if we can!
Each quadrat is 25cm x 25cm.
We know that the total of 10 quadrats is 20 Plantains. Let's forget about quadrats areas for now.
Therefore, in each quadrat we would have a mean of 2 Plaintains.
We want 1m squared, which is a metre x a metre.
4 quadrats in a row would make 1m BUT it isnt 1m2 because its 1m wide but only 0.25m deep (1m x 0.25m = 0.25m squared).
So we want 4 rows of 4 quadrats. Then we'd have 1m wide and 1m deep. 4 x 4 quadrats is 16 quadrats.
We know each quadrat averages 2 Plantains, so 16 x 2 = 32 per M squared.
32 x 5,000 = 160,000
Or does it play no part?