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'Triangle in a Hexagon' printed from https://nrich.maths.org/
Call the length of one side of the hexagon $s$ and the height of
the hexagon $h$:
So the area of the shaded triangle is $$\frac{1}{2} \times s \times
h$$
Now divide the hexagon into $6$ equilateral triangles:
Each triangle has area $$\frac{1}{2}\times s \times \frac{h}{2}$$
so the area of the hexagon is $$6 \times \frac{1}{2}\times s \times
\frac{h}{2}=3 \times \frac{1}{2} \times s \times h$$ or $$3 \times
\text{Shaded area}$$
So the shaded area is $\frac{1}{3}$ of the area of the whole
hexagon.