Answer:
688 cm²/s
Explanation:
You want to know the rate of increase of area of a rectangle that is initially 4 cm by 8 cm, with side lengths increasing at 4 cm/s.
Area
The area is the product of the side lengths. Each of those can be written as a function of time:
L = 8 +4t
W = 4 +4t
A = LW = (8 +4t)(4 +4t)
Rate of change
Then the rate of change of area is ...
A' = (4)(4 +4t) + (8 +4t)(4) = 32t +48
When t=20, the rate of change is ...
A'(20) = 32·20 +48 = 640 +48 = 688 . . . . . . cm²/s
The area is increasing at the rate of 688 square centimeters per second after 20 seconds.