Surface Area and Dimensions of a Tipi

Figure A

 My daughter received a tipi as a gift from her grandfather for her 16th birthday.  This tipi is used for our native american cultural ceremonies.  Time and time again, I observed my relatives set it up for these purposes and I never knew the surface area or the dimensions of this tipi.  The only information I knew was that the diameter is 26 feet and 19 feet in height.  I had no idea how they set it up but I never saw anyone with a calculator or figuring out a math solution for this tipi.

Well... I decided to investigate the set up of this tipi when I learned about dimensions and surface area of a cone.  The surface area of a tipi is shaped like a cone other than the front part that they call ears where smoke escapes from the fire that is built inside.  As you can see in Figure A, I figured about the dimensions by using the Pythagorean theorem.  Then I used the surface area formula to get the results of the surface area.  The end result of what it actually looks like after it is set up (Figure B).

Sources:

Surface Area of a Tipi, Home. Personal photograph by Miranda Tachine-Benally. 2016.

Native American Tipi, Pinon, Arizona.  Personal photograph by Miranda Tachine-Benally. 2016

Tachine-Benally, Miranda.  Personal Measurement Investigation. 08 Oct. 2016. Home. Mesa.

Figure B

The Scorpion and the Cricket

Figure A

Figure B

 I honestly had a hard time with a problem in class today.  This particular problem was a homework assignment in which we (students) had to figure out the shortest route the scorpion can crawl to get to the cricket.  As you can see in my drawings, I have labeled the scorpion and the cricket.  The scorpion is seated in the center of the right wall, 1 feet from the ceiling.  The cricket is seated in the center of the left wall, 1 feet from the floor.  The dimensions of the rectangular room is labeled as the base being 30 feet (a), the height being 12 feet (b), and the width being 12 feet (Figure A).

In Figure B, I unfolded the rectangle into a net and implemented the Pythagorean theorem.  Then I figured out my new dimensions and labeled them accordingly.  Then, I calculated my figures using the Pythagorean theorem which is a² + b² = c².  As shown in Figure B, the end result was 40 with the conclusion that the shortest route the scorpion can crawl to get to the cricket was 40 feet.

Sources:

Net of a Rectangular Room, Mesa Community College. Personal photograph by Miranda Tachine-Benally. 2016.

Tachine-Benally, Miranda. The Scorpion and the Cricket. 03 Oct. 2016. Classroom Worksheet. Mesa Community College, Mesa.