Samantha’s square courtyard (total area less than 100 m^2 ) has an area equal to an integer number of square meters. She decides to install an octagonal fish pond in the courtyard.

To mark the sides of the pond, she draws lines from each corner of the square to the midpoints of the two sides not touching said corner. She finds that the perimeter of the pond, thus delimited, is an integer number of meters.

What is the area of the courtyard, and what is the perimeter of the pond?