The phrase "area encompassing" is correct and usable in written English.
It can be used to describe a specific region or space that includes or surrounds something else.
Example: "The area encompassing the national park is home to diverse wildlife and stunning landscapes."
Alternatives: "region including" or "zone covering".
The area encompassing La Guardia was once home to a beer garden-cum-amusement park.
Mr. Guerriere hopes to draw participants from all of greater Hartford, an area encompassing three-quarters of a million people.
AJ More heads the railway police team in charge of accidents in an area encompassing seven stations.
Parallel to the Apuane ridge lies the Garfagnana, the name for the area encompassing the Serchio valley north of Lucca.
The greater Yellowstone area, encompassing parts of Wyoming, Idaho and Montana, now has a population of 1,500 wolves.
The Bridgnorth region covers a rural area encompassing many small agricultural villages in the southeastern part of the county.
An estimated 25percentt of the about 500,000 Dominicans in the city live in the area encompassing Washington Heights and neighboring Inwood, according to the Census Bureau.
Born in Newark, Mr. Payne has since 1988 been the United States Representative for New Jersey's 10th District, an area encompassing Essex, Hudson and Union counties.
One is the small area encompassing a stretch of Bourbon Street, the main drag in the French Quarter, and a few streets close to it.
The affected waters cover much of the South China Sea, an area encompassing island groups also claimed by Vietnam, the Philippines and others.
For decades, Khun Sa symbolized the seeming impunity of heroin traffickers in the Golden Triangle, the area encompassing the northern reaches of Myanmar (formerly Burma, Laos and Thailandd.
