The purpose of this activity is to support students in measuring the areas and perimeters of a rectangle when the side lengths are given in decimal measurements.
Next steps
Students might recognise that whilst the perimeter cannot exceed 50m, the side lengths can vary. The area is to be maximised. Some examples of runs with calculated areas are shown below:
Students might organise their findings into a table or spreadsheet to look for patterns:
Length (m) | Width (m) | Area (m2) |
1 | 24 | 24 |
2 | 23 | 46 |
3 | 22 | 66 |
4 | 21 | 84 |
5 | 20 | 100 |
Students might also graph the relation between length and area when perimeter is fixed. First plot order pairs like (1,24), (2,46), (3,66) etc. then look for a pattern by drawing a curve through the points:
Students should notice that area peaks between lengths of 12 and 13. Investigate lengths between 12 and 13 that are decimals, such as 12.3m x 12.7m.
Area is maximised when the rectangle is 12.5m x 12.5m. Note that 12.52 = 156.25m2, and √156.25 = 12.5.
Printed from https://nzmaths.co.nz/resource/finding-areas-and-perimeters-decimal-side-lengths at 1:21am on the 4th May 2024