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 math 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 practice solving 8 problems where 2 objects have the same perimeter but different areas. Questions may include those such as: 

James’ sandbox is 8 feet long by 4 feet wide. Tommy’s sandbox has a length of 6 feet. If James and Tommy both have sandboxes with the same perimeter, what are the areas of the two sandboxes? 

Samantha and Carly have playrooms of the same perimeter but different areas. Carly’s playroom is 8 feet long by 7 feet wide. One of the walls in Samantha’s playroom is 5 feet long. Who has the playroom with the larger area?

An answer key is included with your download to make grading fast and easy!  

Tips for Differentiation + Scaffolding 

In addition to independent student work time, use this worksheet as an activity for:

• Guided math groups 
• Lesson wrap-up
• Fast finishers 
• Homework assignment
• Whole-class review (via smartboard)

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

Perimeter Word Problems – Mixed Problem Types

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 also is 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. 

Because this resource includes an answer sheet, we recommend you print one copy of the entire file. Then, make photocopies of the blank worksheet for students to complete. 

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

Turn this teaching resource into a sustainable activity by printing on cardstock and slipping it into a dry-erase sleeve. Students can record their answers with a whiteboard marker, 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. 

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This resource was created by Nicole Ellis, a teacher in New York and Teach Starter Collaborator. 

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