Two of the nation's top five steel makers reported yesterday that their profits increased in 1981.

The fourth-largest, Armco Inc., said net income rose 11 percent to $294.5 million ($4.97 a share) from $265.3 million ($4.73) in the preceding year as sales jumped 22 percent to $6.9 billion from $5.6 billion.

It was the diversified steel and energy company's fourth consecutive record year in sales and earnings.

Fourth-quarter net income totaled $70.1 million ($1.04) on sales of $1.794 billion compared with $63.4 million ($1.13) on sales of $1.550 billion in the same period a year ago.

And Republic Steel Corp., the nation's fifth-largest steel maker, said earnings for the year rose to $190.1 million ($11.75 a share) from $50.9 million ($3.15) in 1980, buoyed by a net gain of $79.1 million on the sale of coal properties and interest from settlement of a federal tax dispute.

Sales were $4.3 billion compared with $3.76 billion in 1980. Shipments rose slightly to 6.5 million tons from 6.29 million.

Earnings for the final quarter dipped 39.6 percent to $21.7 million ($1.34) from $35.9 million ($2.22) in the 1980 fourth quarter. Sales were $975 million, down from $1 billion, and shipments were off 23.3 percent to 1.3 million tons from 1.8 million.

Georgia-Pacific Corp. reported yesterday that profits plunged 65.6 percent in the final three months of 1981 as high interest rates depressed the construction industry.

Earnings for the fourth quarter came to $22 million (21 cents a share) compared with $64 million (61 cents) in the final quarter of 1980. Sales fell 7.6 percent to $1.22 billion from $1.32 billion.

The wood products giant said 1981 earnings fell 34.2 percent to $160 million ($1.51) on sales of $5.41 billion from earnings of $243 million ($2.33) in 1980 on sales of $5.02 billion.

American Airlines, the nation's seventh-largest transportation company, announced yesterday that it returned to the profit column last year, although it suffered a $34.8 million loss in the fourth quarter.

American listed net 1981 earnings of $47.4 million ($1.21 a share) compared with 1980 net losses of $75.8 million. Operating earnings were $72.2 million compared with a 1980 operating losses of $86.3 million.

The fourth-quarter operating loss of $34.8 million reflects a worsening of $32.2 million from the $2.6 million loss in 1980's fourth quarter.

Santa Fe Industries Inc., No. 9 among transportation companies, said 1981 net income was $242.2 million ($2.73 a share), down from $301.8 million ($3.47) in 1980.

Fourth-quarter profits were $55.2 million (62 cents), down from $103.9 million ($1.19). Revenues were $811.9 million, down from $827.1 million.