An apothem of a square is a perpendicular from a center of a square to one of its side.
1. Put a dot at the center of the square. (You can find the center by drawing diagonals from corner to corner. The center is where they intersect).
2. Draw a perpendicular line in any of the four directions to one side of the square.
3. Two apothems of a square (drawn to opposite sides) make a line that is parallel to both (left) sides of the square, a line that is of equal length. If two apothems added together are equal to the length of one side, then one apothem is half of the length.
4. The square perimeter is 40 and it consists of 4 equal parts, then the length of square's side is 10.
5. Then the apothem has length 5.