22. The diagram shows a shaded region inside a regular hexagon. The shaded region is divided into equilateral triangles. What fraction of the area of the hexagon is shaded?
A $\frac{3}{8}$
B $\frac{2}{5}$
C $\frac{3}{7}$
D $\frac{5}{12}$
E $\frac{1}{2}$
22. E In the diagram, the shaded small equilateral triangles have been divided into those which lie within the highlighted large equilateral triangle and the twelve small equilateral triangles which lie outside the large triangle.
Note that the unshaded star shape in the centre of the large triangle is made up of twelve small equilateral triangles, so the small triangles outside the large triangle could be moved into the large triangle so that the large triangle is shaded completely and the rest of the hexagon is unshaded as in the lower diagram.
The lower diagram shows that the hexagon may be divided into six congruent triangles, three of which are shaded and three of which are unshaded. So the required fraction is $\frac{1}{2}$.