Tetrahedrons What are they and how do we use them?

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# Tetrahedrons What are they and how do we use them? - PowerPoint PPT Presentation

Tetrahedrons What are they and how do we use them?. Courtney Shafer and Mellissa Toothman. What is a tetrahedron?. Let’s think about the word tetrahedron. What do you think it means?. The word- Tetrahedron. The word tetrahedron can be broken into 2 parts: tetra and hedron Tetra means:

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### Tetrahedrons What are they and how do we use them?

Courtney Shafer and Mellissa Toothman

What is a tetrahedron?
• Let’s think about the word tetrahedron.
• What do you think it means?
The word- Tetrahedron
• The word tetrahedron can be broken into 2 parts: tetra and hedron
• Tetra means:

four

• Hedron means:

a crystal or geometric figure having a specific kind or number of surfaces.

Make sense yet????

Put it all together…
• When you put all of that together you get the full definition for what a tetrahedron actually is :
• A tetrahedron (plural: tetrahedra) is a polyhedron composed of four triangular faces, three of which meet at each vertex. Based on a pyramid shape and is the strongest structure known.
Let’s make our own tetrahedron.

Make a Tetrahedron from a Small Envelope

• Here is a simple way to make a tetrahedron from a small envelope.
• All you need is a small envelope, a ruler, a pencil and scissors.
Instructions
• Open the flap of a small envelope.
• Using a ruler and a pencil, mark the diagonal lines from each corner to the opposite corner.
• Mark a third vertical line through the middle of the envelope.
• Fold along each of the lines.
Then…
• Cut along the top two "V"-shaped lines (discard the top of the envelope).
Next…
• Open up the envelope, flattening the bottom a bit.
• Tuck one side of the envelope into the other side.
And Finally…
• You have a tetrahedron!
• To decorate it: untuck it, draw on the sides (but not on the tucked-in side), then re-tuck one side in.
Now what???
• Now we have discussed what a tetrahedron is, made an example, and know about all of it’s characteristics.
• Let’s talk about how we can use tetrahedrons.
But first, some history…
• It is part of Bell's legend that he made his most important discoveries on accident.
• The telephone was an accidental invention that came from the telegraph!
• The tetrahedron grew out of his search for a flying machine.
A kite?!?!
• Bell hoped to develop a kite large enough to carry a man.
• How could he increase the size without increasing the weight?
• With this question, Bell took his first step on the road to the tetrahedron .
Bell removed sides which decreased the weight of the kite.
• Moreover, a triangle is a more stable shape than a rectangle, which tends to distort in the wind.
• By adding many small surfaces, Bell increased the total surface area, with little increase in weight.
• This was the tetrahedron, one of nature's most stable structures.
• His invention looked something like this…
Bell’s kite’s are now displayed for the public to view.
• The kite’s are on display in Baddeck, Nova Scotia.
What does all of this mean?
• Bell had trouble constructing the flying machine for many reasons.
• One of which being the materials he was using were taking up too much space.
• The amount of space an object takes up is called it’s surface area.
Surface area of a tetrahedron…
• It’s not too hard, you just have to remember this formula:

b= base

h=height

a= area of a side

2

• Here are some example problems.
• Work with a partner to try and figure our what the surface area would be for these tetrahedrons.

Example 1- b=8 cm, h=4 cm, and a=10 cm

Example 2- b=5 cm, h=6 cm, and a= 12 cm

What else???
• What else can we do with a tetrahedron?
• What other things are shaped like or have similar design to that of a tetrahedron?
Bell’s Challenge
• Now… we are going to construct and actually FLY a tetrahedron kite!!!!
Outcomes