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.



Gumdrop Polyheras

Cube

Square Pyramid

Pentagonal Prism

 Building gumdrop polyhedrons with colored toothpicks and spicy gumdrops was a blast!  This project was part of a unit in our Geometry chapter of our mathematics book.  The goal of this "Centers" activity was to build polyhedrons while paying close attention to the number of faces (the flat surfaces), vertices (corner points), and edges (line segment which joins two vertices).  Furthermore, we had to give an example of, "Where in the World" these polyhedrons exist.  Although, it looks simple, it was actually a brainstorming activity for me as I have not been aware of the many polyhedrons that exist.  The three pictured here are a few of many!

So... for the cube, I indicated there was six faces, eight vertices, and twelve edges.  "Where in the World" can this be found is in our kitchen cupboards with the label "Sugar Cubes."  And for the square pyramid, I indicated there was five faces, five vertices, and eight edges.  It can be found in Giza as an Egyptian Pyramid.  Can you figure out the faces, vertices, and edges for the pentagonal prism?  And, "where in the world" it can be found?  There is a formula called Euler's Theorem that is very helpful.  This formula is V+F-E=2.  Meaning Vertices + Faces - Edges = 2.

Sources:

Gumdrop Polyhedras, Mesa Community College. Personal photograph by Miranda Tachine-Benally. 2016.

Tachine-Benally, Miranda. Resource Sheet 4 a. 7 Sept. 2016. Classroom Worksheet. Mesa Community College, Mesa.