Final answer:
The combined estimated number of deaths due to the building of the Panama Canal during the French and United States projects is approximately 25,600 to 26,000.
Step-by-step explanation:
The estimation of the number of deaths associated with the construction of the Panama Canal includes the lives lost during both the French and United States efforts. Under the French administration, headed by the well-recognized engineer Ferdinand de Lesseps and later Gustave Eiffel, the project encountered many difficulties such as tropical diseases and challenging working conditions. These adversities led to the death of over 20,000 workers before the project was eventually abandoned. When the United States took over, they introduced measures to combat diseases like malaria and yellow fever, yet still, about 5,600 more lives were lost during their phase of the canal construction. Therefore, combining the fatalities from both the French and the United States projects, the estimated total deaths is approximately 25,600 to 26,000.