In parallelogram ABCD AB = AD = BD, the height is h. Find the area of the parallelogram.

Consider a triangle ABD. It is clear from the condition that it is equilateral.
Once in a parallelogram the opposite sides are equal, then we prove that:
S abcd = 2 • S abd.
Find the area of the triangle ABD by the formula: S = ½ a • h, where a is the base of the triangle. Substitute the values and get:
S abd = ½ AD • h;
Find the AD side using the formula and find out that:
AD = 2h / tg (A), therefore:
S abd = h • h / tg (60) = h² • √3
From here we find the area of the parallelogram:
S abcd = 2 • h² • √3