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).
The three corners of a triangle are sitting on a circle. The angles
are called Angle A, Angle B and Angle C. The dot in the middle of
the circle shows the centre. The counter is measuring the size of
Angle A in degrees. What is the smallest Angle A can be? What is
the largest Angle A can be? What else do you notice about Angle A
as you move the corners of the triangle around the circle?
Remember that folding an equilateral triangle in half gives you
a 30-60-90 triangle and the ratios of the lengths of the sides.