The rate of increase is found by differentiating with resepect to time. The product rule comes into play here.
A = LW
dA/dt ≈ (dL/dt)·W + L·(dW/dt)
... = (6 cm/s)·(5 cm) + (7 cm)·(3 cm/s)
... = 30 cm²/s + 21 cm²/s
... = 51 cm²/s . . . . rate of area increase