The phrase "area to work" is correct and usable in written English.
It can be used to refer to a specific space or environment designated for work-related activities.
Example: "We need to find a quiet area to work on our project without distractions."
Alternatives: "workspace" or "work zone".
At first each curator was given an area to work on.
"Love and sex has always been a tricky area to work out.
"It's our main area to work in the winter," he said.
Come the 1990's, it became a more pleasant area to work and live.
It's a complex area to work in – 85,000sq km of jungle.
It is a popular area to work in, with many advertised posts receiving several hundred applicants.
At home have a good desk and lighting in a quiet area to work at.
Upon graduation, she moved to the Bay Area to work in business and finance.
Many who'd been racing up ladders in New York or Los Angeles or Washington dropped everything and moved out to the Bay Area to work.
I was 14 when I came to the Bay Area to work at Netscape (socially stunted badge pic below).
After about two years, Wexler moved to the Palm Springs area to work for modernism architect William Cody.
