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I read 13d together with 19d as a hint for how to calculate the lengths of two sloping legs in the desired shape.

My understanding is that the bottom row refers to a 7a in which two measures of its size are equal. I believe there is one of those which has a right angle, satisfies the preamble and occupies an exact proportion of the grid.

Bearing in mind the angle between the diagonal and the top border, I don't see how the shape can have a right angle and two equal measures. There is a shape with a right angle but without equal measures, but it only uses part of the diagonal, which is not what the preamble says.

As for 13d and 19d, they apply to shapes outside the required shape. Strictly speaking, either one of them is sufficient on its own to provide the clue for the necessary calculations, but they are both relevant.

I think I now understand. You interpret the preamble as meaning that we have to use all of the diagonal. I think it can also be read to allow using part of it starting from cell 1, which allows for a much more straightforward answer which complies with all of the perimeter entries.

And has two equal measures.

Maybe we are at cross-purposes, but it is not possible for a 1a and 7a to have a right angle and two equal measures. One of the sides would have to be a multiple of the square root of two.

The measures I was meaning are referred to as A and P in relation to the bottom row.

ozzy, perhaps you do not have the correct answer to the "55/56"? There are no "1a/7a" that have A&P equal to the answer to the "55/56". If you google the question, the correct dimensions should be clear.

sorry, it should be no "1a/7a" containing a right angle that have A&P equal tio.....

I think that as the preamble states to use THE diagonal and PART OF THE top border there is no ambiguity about the intended shape.
If it was intended that part of the diagonal would suffice then surely the preamble would have said so, or not included the statement about part of the top border.
There are 12 1a 7a s with an area of less than 56 and many of them have the same angle defined by the use of the diagonal and the top row.
Only one utilises the whole diagonal though and it has an area related to 55, 56. While not an example of 19 down it can be constructed by removing one 19 down from another - both of which as it happens are examples of 1,7.