While surveying a square field, a clerk records its side as 5% longer than it really is. By what percentage will the area he calculates exceed the true area?

The recorded side is 1.05 times the true side, so the recorded area is $1.05^2=1.1025$ times the true area, i.e. 10.25% too large. The trap 5% carries the linear error straight across to the area; 10% doubles the 5% and quietly discards the 0.25% that squaring adds; 25% squares the number 5 rather than the factor 1.05.