In the Treaty of Deogaon signed in 1803, the British acquired the area of Cuttack. Cuttack is a city located in the present-day state of Odisha in India. It was an important trading center during the medieval period and was known for its maritime activities and connection with Southeast Asia. The acquisition of Cuttack by the British through the Treaty of Deogaon marked a significant expansion of their territorial control in India.

Now let`s dissect the other options to understand why they are incorrect:

Option 2: Murshidabad - Murshidabad was the capital of Bengal during the Mughal period, but it was not acquired by the British under the Treaty of Deogaon.

Option 3: Surat - Surat was an important port city during the Mughal era, but it was not acquired by the British under the Treaty of Deogaon.

Option 4: Calicut - Calicut, also known as Kozhikode, was an important trading center in Kerala, but it was not acquired by the British under the Treaty of Deogaon.

Therefore, the correct answer is option 1 - Cuttack.