The length of the rectangle is 25 and the width is 20. If the length increases by 6 and the width increases by 4, find the increased rectangular area.

Analysis:

This is a rectangular area problem, which is not difficult, but easy to make mistakes. It is easy to calculate directly from 6×4=25 according to the habit, and take the result as the increased rectangular area. Actually, this is not right. As shown in the figure below, the actually increased rectangular area includes ①-③ three parts, and 4×6=25 is only ① the actually increased area, and ② ③ is also the increased area. This is the wrong thing to do.

Answer:

As shown in the figure, the actually increased rectangular area is:

4×6+6×20+4×25

=24+ 120+ 100

=24+220

=244

This is the actual increase in area.

This problem can also be calculated as follows:

(25+6)×(20+4)-25×20

=3 1×24-25×20

=620+ 124-500

= 120+ 124

=244

It can be seen that the two calculation results are consistent, which also shows that 244 is the real increased area.