In a parallelogram,

opposite sides are parallel, and equal; opposite angles are equal, and the diagonals (lines inside that intersect) bisect each other.

When you know the length of the diagonals, half of them would be the sides of a traingle they form with one of the sides of the parallelogram.

Use the theorems that (i) when two lines intersect each other, the vertically opposite angles are equal and (ii) sum of the total angles is equal to 360 degrees. This way, all the angles can be known.

Now, use the Cosine Theorem

a² = b² + c² - 2bcCosA

(where A, B, C are three angles of a traingle and a,b,c are the three sides opposite to angles A,B,C respectively)

for knowing the third side of the triangle, which forms a side of the parallelogram. Following this method, the adjacent side too can be found! Since opposite sides of a parallelogram are equal, we know all the four sides!

I know this reply is long, and may not be of much help; that's because some Mathematical problems are difficult to explain without a diagram!