Explanation:

Dudhwa National Park, located in the Terai belt of Uttar Pradesh, covers an area of approximately $490 \text{ km}^2$. It is known for its rich biodiversity, including tigers, leopards, and a significant population of barasingha (swamp deer). Options (1) $270 \text{ km}^2$, (2) $310 \text{ km}^2$, and (4) $510 \text{ km}^2$ are incorrect measurements for the total area of Dudhwa National Park. The precise area is crucial for understanding the park's ecological capacity and conservation efforts. Hence, $490 \text{ km}^2$ is the accurate figure.