Approach

Written by Isaiah Iliffe from CSESoc Education

This is a maths problem, and once you find the idea for a formula, the code required is simple.

One elegant solution involves first observing that the honeycomb shape can be viewed as a large equilateral triangle, with three smaller equilateral triangles removed from its corners. Thus the total area of the honeycomb can be calculated by subtracting areas.

Suppose the large equilateral triangle's top edge is horizontal. Then the smaller removed triangles have side lengths $B-1$, $F-1$ and $D-1$, since their edges are one away from the sides of the hexagon, so their lengths are shorter by one cell. The large triangle has side length $A+(F-1)+(B-1) = A+B+F-2$, since its side length of the top edge is $A$ plus the side lengths of the removed triangles on each side.

Finally, to compute the areas easily, we can use the triangular numbers. This is all reflected in the sample code.