The question asks us to identify which factor does not influence the extent of damage caused by an earthquake. Let`s analyze each option to understand their role in earthquake damage.

Option 1: Strength of earthquake. This option suggests that the magnitude or intensity of the earthquake does play a significant role in determining the extent of damage. Generally, stronger earthquakes result in more severe damage.

Option 2: Population density. This option implies that areas with high population density are more likely to experience more damage during an earthquake. This is because densely populated areas often have more buildings and infrastructure that can be affected.

Option 3: Type of building. This option indicates that the type and quality of buildings can affect the extent of damage. Well-designed and earthquake-resistant structures are more likely to withstand the seismic forces, reducing the damage compared to poorly constructed buildings.

Option 4: Climate of the area. This is the correct answer. The climate of an area, such as temperature or precipitation patterns, does not have a direct impact on the extent of damage caused by an earthquake. Earthquake damage is primarily determined by factors like earthquake strength, population density, and building types.

In conclusion, out of the given options, the climate of the area does not influence the extent of damage caused by an earthquake.