Answer:
-204 km^2/min
Step-by-step explanation:
For base edge length s and height h, the surface area of the prism is ...
A = 2(s^2 +2sh) = 2s^2 +4sh
Then the rate of change of surface area is ...
A' = 4s·s' +4s'·h +4s·h' = 4s(s' +h') +4s'·h
Filling in the given values, we find the rate of change of area to be ...
A' = 4(4 km)(-7 km/min +10 km/min) +4(-7 km/min)(9 km)
A' = 4(12 km^2/min -63 km^2/min)
A' = -204 km^2/min
The area is decreasing at the rate of 204 square km per minute.
