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

Surface Area Activity

Trapezoidal Prism

 Activity in my MAT 257 was somewhat interesting today because we got to find surface areas engaged in a hands-on group activity.  My group got the more difficult of five shapes, Trapezoidal Prism.  The other shapes were hexagonal prism, rectangular prism, truncated square pyramid, and a cylinder.  We were instructed to examine the shape, identify the shape, develop a plan for finding the surface area of the shape, perform calculations showing all steps, and label with proper units.  The tools given to us by the instructor was a worksheet, a ruler, a post-it poster, and a marker. 

Our first approach after identifying the shape was to identify how many faces our shape had and label it with an alphabet.  Our shape had six faces so we labeled it A through F.  Then, we had to determine what kind of shapes we would reveal if we could unfold it.  We determined that we would have two trapezoids and four squares.  Next, we had to figure out what formulas would accommodate us in figuring out our surface areas.  We came to the conclusion that our A and B sides, shaped like a trapezoid, would use the trapezoid formula of:  A=1/2h(b1+b2).  Our C, D, E, and F would be calculated using the rectangle formula which is, A=bh (Area = base X height).  As you can see, we had fun with it and we nailed it!! :)


Surface Area of a Trapezoidal Prism

Sources:

Surface Area Gallery, Mesa Community College. Personal photograph by Miranda Tachine-Benally. 2016.

Tachine-Benally, Miranda. Surface Area Activity. 28 Sept. 2016. Mesa Community College, Mesa.