"only a small area" is correct and usable in written English.
You can use this phrase to emphasize that a certain place is limited in size. For example: "The town was only a small area, but it was full of life and energy."
(The excavation covered only a small area of Dinaledi).
But Smarr's gastroenterologist was skeptical: a colonoscopy had shown only a small area of inflammation.
Only a small area along the rivers in the south is cultivated in rye, potatoes, oats, barley, and vegetables.
That may be because Opportunity has examined only a small area, or it may reflect a difference in how the concretions formed.
The straw was in contact with bread through only a small area, from the top of the piece to the bottom.
Mughal rule was reduced to only a small area around Delhi, which passed under Maratha (1785) and then British (1803) control.
Down in Ciego de Avila, Cuba's best orange-growing province, they claim yields from the organic plantations - still only a small area - are 20% higher.
Because of the density of the buildings in New York City, the trucks could serve only a small area, according to Mr. Ray.
The villages cover only a small area, perhaps as little as 100 square miles, but Kurdish officials believe access to the border could explain the recent growth of the group.
He reminded his audience, which included the Chief Rabbi, the Rev Dr Immanuel Jakobovits, that the holy city was only a small area, a little more than one kilometre square, with 26,000 people living inside it.
When Sonni ʿAlī ascended the Songhai throne c. 1464, the kingdom comprised only a small area in the upper Niger valley around its capital, the prosperous trading city of Gao.
