Forming equations from shape and facts we know about shape is a really important skill and it is a skill that can prove quite challenging for some students. Other students are able to take to this without much of a struggle. I produced these questions to challenge their reasoning and their awareness of the properties of the shapes.
These problems can be made by working out each individual side length, collecting them and equating your expression to the given perimeter however they can be made much easier by students recognising that the rectangles can be shifted to the side and that you can 'ignore' parts of the perimeter if you'll have to subtract the same length further down the line because of another part of the shape.
The shapes begin quite straight forward to encourage all students to get started and to feel some success.
The questions increase in difficulty now that they're comfortable labelling the sides they have and collecting like terms.
Once students have become more confident with knowing that they now need to subtract expressions they then face the following:
I like tasks like these as the next step is for a student to work on their own compound shapes using congruent shapes. The students seemed to enjoy the challenge from these questions and impressed me with how they took to the harder problems.
For a downloadable copy: https://drive.google.com/file/d/1o_7Sil-kNF72Yd-dhE7ZIlSCpEIpPJhQ/view?usp=sharing