Same Perimeter, Different Area Word Problems

Have your students mastered the basic concepts of perimeter and area? If so, they may be ready for more challenging maths problems where they have to use multiple operations to solve a problem. These multi-step word problems will give your students an opportunity to answer questions where they have to use the perimeter of one object, determine the missing side length of another object, and then calculate the area.

With this worksheet, students will have the opportunity to practise solving 8 problems where 2 objects have the same perimeter but different areas. Questions are similar to the following:

James’ sandpit is 4 metres long by 2 metres wide. Tommy’s sandpit has a length of 3 metres. If James and Tommy both have sandpits with the same perimeter, what are the areas of the two sandpits? 

Samantha and Carly have playrooms of the same perimeter but different areas. Carly’s playroom is 6 metres long by 8 metres wide. One of the walls in Samantha’s playroom is 5 metres long. Who has the playroom with the larger area?

An answer key is included with your download to make marking their work fast and easy!  

Tips for Differentiation + Scaffolding 

For students who need a bit of a challenge, consider assigning one of the additional versions of this resource:

Unknown Side Perimeter Word Problems

If there are students who need support, consider completing this worksheet in a 1-on-1 setting or in a small group setting. Additionally, work with students to draw a picture to solve each problem. There is also a version of this resource where students practice solving standard perimeter problems.

🖨️ Easily Download & Print

Use the dropdown icon on the Download button to choose between the PDF or editable Google Slides version of this resource. 

To save paper, we suggest printing this 2-page worksheet double-sided.

Turn this teaching resource into a sustainable activity by printing it on card and slipping it into a write and wipe sleeve. Students can record their answers with a whiteboard marker and then erase and reuse them. 

Additionally, project the worksheet onto a screen and work through it as a class by having students record their answers in their notebooks. 

This resource was created by Nicole Ellis, a Teach Starter Collaborator. 

Don’t stop there! We’ve got more activities to shorten your lesson planning time: