Find the area of a triangle with a base of 5 cm and a height of 8/9 cm.

The area S of any triangle is calculated by the formula S = a * h / 2, where a is the length of the base of this triangle, and h is the length of the height of the triangle dropped on this base.
According to the condition of the problem, the length of the base of this triangle is 5 cm, and the length of the height dropped on this base is 8/9 cm, therefore, the area S of this triangle is:
S = a * h / 2 = S = 5 * (8/9) / 2 = 5 * 4/9 = 20/9 = 2 2/9 cm².
Answer: the area of this triangle is 2 2/9 (two integers and 2/9) cm².