A floor is covered by a tessellation of equilateral triangles, each having three equal arcs inside it. What proportion of the area of the tessellation is shaded?
Investigate the different ways of cutting a perfectly circular pie into equal pieces using exactly 3 cuts. The cuts have to be along chords of the circle (which might be diameters).
How can you make an angle of 60 degrees by folding a sheet of paper
This problem invited students to
consider the relationship between opposite angles of cyclic
quadrilaterals. Often, with these types of problems, it is helpful
to draw diagrams; several students submitted diagrams as part of
their solution - well done.
The problem is divided into two parts: the
first part contains questions that form "building blocks" to help
meet the final challenge in the second part.
Nick, from St Stephen's at Carramar summed up
Click here to see his full
solution with diagrams.
Well done also to the following students, who
also submitted similar (and correct!) answers to this problem:
Andre, Laura, Sascha, Chris and Sailesh from St. Stephen's School,
Marcus and Kye from St Philip's Primary School, and Natasha.
Now that you have completed this
problem, you could try the following problems as an
extension: Subtended Angles and/or Right Angles.