Triangle Tents

The basic question:  If you fold a notecard along a line of symmetry and then make a 'pup tent' using that notecard,

how do you position the legs to make the tent that has a maximum volume?

Background:

Classic Fence problem

Framer Brown has 120 feet of fence to build a pen for his cows.  He wants to make a rectangular pen that gives his cows the most room to graze.  What dimensions should he make his pen to use all his fencing and give his cows the most room?

The original tent problem

Take a standard 4x6 index card and fold it down the middle of the longest side.

This gives us our tent. By moving the tent legs closer together and further apart we will get various tents of different volumes.

  What is the largest volume that you can get from this tent?

*Show your work, solution and explanation in the space below:

Make sure to indicate the dimensions or instructions needed to make this particular tent:

Diagram of the Problem

Various solutions including:

number/table using b--->excel

Volume in terms of the base (b)

Volume in terms of the height (h)

Volume in terms of the vertex angle (theta)

Volume in terms of the base angles (alpha)

A trigonometric approach              Remember:  (1/2)absinC

Student Work

Some Related Calculus

Summary of results and Visualizing using Desmos

A picture and some reflection using Geogebra

Tent Problem And extensions

Assessment for tent problem

Summary/conclusions                                                                                 The Paper

Related research