Triangle Area Calculation: Can We Find Area with BC=5cm and AD=4cm?

To determine whether it's possible to calculate the area of triangle $ABC$ with the given side $BC = 5$ cm and segment $AD = 4$ cm, we need more information than currently provided.

The possibilities for calculating the area of a triangle generally rely on knowing:

• the base and the corresponding height
• all three sides
• two sides and the included angle

In this problem, we lack sufficient data to directly apply any of these methods. Specifically:

• We do not know if $AD$ is perpendicular to $BC$, which would make it a height usable in the base-height formula.
• We only know one full side, $BC$, and a segment, $AD$, but no additional sides or angles.
• Without confirmation that $AD$ serves as an altitude or precise geometric location or measurements of angle $\angle BAC$, further calculations can't proceed.

Thus, with the given information, we cannot conclusively determine the area of triangle $ABC$.

Therefore, the solution to the problem is it is not possible.