A quick little geometery puzzle this week, shown to me by a friend. It's not too challenging.

If the regular hexagon above is one square unit, what is the area of the yellow quadrilateral?

Answer

It looks complicated at first but, actually, we don't need to worry about angles, we can simply work with symmetry. The hexagon contains six equilateral triangles (shown in red below). Each of these triangles is 1/6 of the area of the large hexagon.

Each of these triangles can be sub-divided into three identical kite shapes. Each of these kites is 1/3 of the area of the triangle.

The quadrilateral we are seeking is one of these.

Combining these, the yellow quadriteral has an area of 1/3 × 1/6 = 1/18 the area of the hexagon.

The quadrilateral has an area 1/18th the area of the hexagon.

Update

It's been brought to my attention that almost exact copy of this puzzle was published a few months ago on the great site Brilliant.org (this might even have been the source of the puzzle that my friend showed me).

If you these kinds of puzzles, their site is a treasure trove. I highly recommend it.