Construction has begun on a new three-story office building, The Westex, located at 1375 Piccard Drive near the I-270 Shady Grove exit in Rockville. Completion of the project is scheduled for early 1984.

The 112,500-square-foot building was designed in an "X" shape to produce more windowed offices. iccard Associates of McLean are the owners and developers of the Westex building and financing for the project was provided by Dominion Bankshares Mortgage Corp. of Fairfax. The James G. Davis Construction Corp. of Rockville is the general contractor.

Other recent developments in commercial realty in the Washington metropolitan area:

The Westwood Center II, a retail and office complex at 5110 Ridgefield Road in Bethesda, has opened its ground-floor retail space. The two-story building opened its 20,150 square feet of upper-story office space last August.

The Westwood Center II is a sister building to the Westwood Center I, a shopping center with 14 stores across the street at the intersection of Ridgefield Road and Westbard Avenue. The Westwood centers are owned by Westwood Joint Ventures, Bethesda real estate developers.

The Westwood Center II contains 20 stores within 30,300 square feet of retail space. Merchants include The Candy Bar, Chase Gifts, Chelsea Florists, Gallery Petalouth Ltd., Kenwood Jewelry, Kenwood Custom Tailors, Pierdonati of Roma, the Adjustable Bed Co., Laurie's of Westwood, the Lemon Twist, Martin Design Group, Nita's, Razi Studio, Sunshine Hair Studio, VIP Travel, West River Deli, the Spa Lady and the Safe Depository of Washington. he center also includes branch offices of Citizen's Bank and Trust Co. of Maryland and Standard Federal Savings & Loan Association.