Problem of the Week 14

A six-pointed regular star consists of two interlocking equilateral triangles.  What is the ratio of the area of the entire star to the area of one of the equilateral triangles?

wk14

Alternate Problem 14

A regular hexagon with sides measuring 1 unit can be separated into 6 equilateral triangles with 1-unit sides.  Show how.

How many equilateral triangles with 1-unit sides can be drawn in a regular hexagon with sides measuring 2 units each?  Show how.

 

Extension Problem 14

Three points not in a straight line are drawn in the plane.  If a fourth point is selected, where must it be properly located so that the four points may form a convex quadrilateral?  Where must the point be located so that it is not possible to form a convex quadrilateral?