The top and bottom of this solid are regular hexagons, and the 12 faces are isosceles trapezoids. The "toy" can be used as a mini-review sheet, for students to use in studying the formulas for volume and surface area of solids (or for reviewing any other topics).

The trapezoidal faces on this pattern are blank, so that students can choose their own topic to review. The 3-dimensional model shows the HexaTrapezoidal solid with the formulas for volume and surface area of geometric solids.

The pattern is left blank, so that students can write in their own questions and answers. Research has shown that the act of writing information down reinforces it in memory, and helps students learn the material.

The HexaTrapezoidal solid flattens out so that it can be carried easily in a notebook or ring binder. It is small enough for student to carry in a shirt pocket, and take out for a few minutes of review while in a lunch line, or in a car on the way to school.

The pattern for this 3-dimensional project is shown here:

:

The pattern shown below has the theorems written on it. However, if time permits, it would be much better for the students to write the theorems themselves. Research has shown that the process of writing information on paper actually helps to reinforce the concepts and help the students to remember them.

When the two halves of the hexatrapezoid are attached, they will form a 3-dimensional solid that looks like the one below:

This model can be opened up to look like the picture above (but with the theorems on it). Then it can be flattened (by pushing down on the top), so that is flat and will fit into a notebook or pocket. The student can than take the hexatrapezoid "reviewee" out, while on the bus or at home, to study the theorems.

And here are the answers to the "Geometric Castle" from the previous lesson (8.1):

Area (all in square units):

1) 1) 600

2) 9 times the square root of 5

3) 18 pi

4) 300 pi

5) 14,000

6) 9 times the square root of 5 divided by 2, times pi

7) 450

8) 9 times the square root of 39, divided by 4

9) 300

Volume (all in cubic units):

1) 450

2) 9

3) 18 pi

4) 450 pi

5) 150,000

6) 9 pi

7) 450 pi

8) 9 times the square root of 3, divided by 4

9) 225 times the square root of 3, divided by 2