Aetna said it will buy Coventry Health Care for about $5.7 billion in cash and stock, a move that Aetna said would help it expand further into government-backed programs like Medicaid and Medicare. The acquisition would be the biggest in the managed health care industry since the Affordable Care Act was signed into law in 2010. Under the terms of the deal, Aetna, which is based in Hartford, will pay $27.30 in cash and 0.3885 of a share for each of Coventry’s shares. Coventry, based in Bethesda, Md., offers a variety of insurance services, including government-financed programs. It earned $543.1 million last year on revenue of $12.2 billion, and its shares rose 17.5 percent in the 12 months before the deal was announced.