Hello, Zellator!

If we are allowed to use Trig, I have a solution.

The diagonals of a parallelogram are 16 and 20.

One side of the parallelogram is 12.

Find the area of the parallelogram.We have parallelogramCode:D C o * * * * * * * o * * * * * * 8 * * * * E * 10 * * ♥ * * 10 * * * * * 8 * * * * * * o * * * * * * * o A 12 B

. . with diagonals

. . which are bisected at

Consider triangle

Let be the altitude fromCode:E o 10 * : * 8 * :h * * @ : * A o * * * * * * * * * * * o B 12

Let

. .