CPC 02 (Challenge Problem Challenge)
Skills I Used
• Used variables to represent quantities and set up equations (I used the variables h, H, and e.
These helped tremendously in discovering the area of the larger hexagons.)
• Auxiliary lines: added a line or lines to the diagram to help in solving the problem (I used
auxiliary lines in the larger hexagons and in the red triangle.)
Assessments Page 1
auxiliary lines in the larger hexagons and in the red triangle.)
• Used appropriate technology: used Desmos, a calculator, or measuring tools strategically (I
used a calculator briefly to check some of my calculations.)
In the first half of this problem, I used variables to set up equations that showed the
relationships between the side lengths of the smaller hexagons, the larger hexagons, and the
small equilateral triangle in the middle of everything. Using those equations, I was able to find
the area of the larger hexagons.
Next, I discovered that the red triangle is 2/3 the area of one of the larger hexagons by
reorganizing the triangle into a rectangle inside the hexagon. Using this and the area of the
larger hexagons, I could calculate the area of the red triangle.
Forming solutions visually, which I used primarily for the second half of this problem helps
tremendously in more challenging problems like these. I tend to use more algebraic paths in
problem-solving, and I find it can be very good to get more comfortable with visual solutions.
Assessments Page 2