In the parallelogram, the product of adjacent sides = 27 cm, and the product of the heights drawn to them is 12 cm. Find S -area.

Let’s denote the sides of this parallelogram as a and b, respectively, the heights drawn to them will be ha and hb.
Let’s use the formula for the area of a parallelogram and write:
S = a * ha = b * hb.
According to the condition of the problem, we are given the products of adjacent sides and the product of heights drawn to them:
a * b = 27 (cm);
ha * hb = 12 (cm).
Multiplying this data, we get the square of the parallelogram area:
S² = a * b * ha * hb = 27 * 12 = 324 (cm ^ 4).
Accordingly, S = √324 = 18 (cm²).
Answer: the area of the parallelogram is 18 cm².