The side of the square is 10 dm. Find the approximate increment of its area when the side increases by 0.1 dm.

The increment is the difference between the values of the areas of the enlarged and the original squares. Let’s first find the area of the original square:

S = 10 x 10 = 100 (dm²).

Now we find the area of the enlarged square with a side of 10.1 dm:

S ‘= 10.1 x 10.1 = 102.01 (dm²).

Now let’s find the actual area increment:

S ‘- S = 102.01 – 100 = 2.01 (dm²).

Answer: when the side increases by 0.1 dm2, the area increases by 2.01 dm².