Education Technology

Triangle Areas

Activity Overview

A triangle circumscribes a rectangle. The triangle is not unique, so what is the minimum area of the triangle that circumscribes the triangle? Students use the dynamic representation on TI-Nspire, data capture and more to explore this problem with some elegant solutions. 


The purpose of this activity is for students to combine some straight forward geometry (similar triangles) to establish a formula for the area of a special triangle so they can use calculus to determine the minimum area. 


  • Similar triangles
  • Derivative (rational function)
  • Minimum

About the Lesson

Students use a dynamic representation of a geometry problem, collect (generate) data and then use their equation to model the data. Once the equation is confirmed, students use differential calculus to determine the minimum area.