South African Mathematics Olympiad First Round

By joining opposite vertices, the hexagon can be divided into six congruent equilateral triangles. If we form a rectangle around the hexagon by drawing lines through $A$ and $B$ parallel to $CD$, then the area of the rectangle is $AB\times CD$. Next, the portion of the rectangle outside the hexagon is composed of four right-angled triangles, which can be combined into two equilateral triangles congruent to the first six. Thus the area of the rectangle is $\frac{8}{6}\times 126=168$, which is also equal to $AB\times CD$.