In measuring the sides of a rectangle, one side is taken 10% in excess, and the other 8% in deficit. The error percent in the area calculated from these measurements is:

Let the original length be l and the original width be w. The original area is A=l×w.
New length = l×(1+
100
10
​
)=1.1l

New width = w×(1−
100
8
​
)=0.92w

The new calculated area is:

A
new
​
=1.1l×0.92w=1.012lw=1.012A
The error fraction in the area is:

Error=A
new
​
−A=1.012A−A=0.012A
The error percentage is:

Error Percentage=0.012×100=1.20%
Alternatively, using the successive percentage formula a+b+
100
ab
​
where a=+10 and b=−8:

Net Error%=10−8+
100
10×(−8)
​
=2−0.8=1.20%
Since the result is positive, it means there is a 1.20% excess error.