The lengths of the diagonals of a rhombus are 18 cm and 24 cm. What is its perimeter and what is the distance between the parallel sides?

The half-diagonals are 9 cm and 12 cm, so the side length can be computed by the Pythagorean theorem as
  √(9^2 +12^2) = √225 = 15 . . . . cm

The figure has 4 sides of this length, so the perimeter is 60 cm.

The area is computed as half the product of the diagonals, so is
   (1/2)*(18 cm)*24 cm) = 216 cm^2. It is also computed as the product of the side length and the distance between sides. Then the distance between parallel sides is
.. (216 cm^2)/(15 cm) = 14.4 cm