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
Thanks to Georgie and Makenzie who pointed out that:
Eastlea Community School went a little further and worked out that:
Kirsty from Hertfordshire and Essex High School used this to help her find the angles of the two triangles that appear at the end of the problem:
The pink triangle is made up of three isosceles triangles.
This makes the 3 angles of the pink triangle 60 degrees (50
degrees plus 10 degrees), 40
degrees (10 degrees plus 30 degrees) and 80 degrees (30 degrees plus 50 degrees).
The blue triangle is made up of two isosceles triangles minus one
This makes the 3 angles of the blue triangle 120 degrees (70 degrees plus 50
degrees), 40 degrees (70 degrees minus 30 degrees) and 20 degrees (50
degrees minus 30 degrees).