Education Technology

Algebra II: Maximizing the Area of a Garden

by Texas Instruments


  • Students will determine the relationship between the width and length of a garden with a rectangular shape and a fixed amount of fencing. The garden is attached to a barn, and exactly three sides of the garden will be fenced.
  • Students will determine a formula that can be used to compute the area of the garden when given the width.
  • Students will find the dimensions of the garden that has the maximum possible area.


  • perimeter
  • area
  • maximize
  • conjecture

About the Lesson

In this activity, students explore the area of a garden with a rectangular shape that is attached to a barn. Exactly three sides of the garden must be fenced. Students will sketch possible gardens and enter their data into a spreadsheet. A guided lesson video (optional) is also available for this activity. The video is targeted at students and designed to help guide them through the interactive exploration and the concepts covered within. (It may also be helpful for teachers who may be using the activity for the first time.) 
As a result students will:

  • Graph the data, find an equation for the area of the garden in terms of its width, find the maximum area of the garden, and solve related problems.
  • Determine that, given a fixed perimeter, the area enclosed depends upon the dimensions chosen.

The extension problem provides an opportunity for students to explore a different scenario—a garden with a rectangular shape that must be fenced on all four sides. Problem 2 in the TI-Nspire™ document may be used to explore this scenario.