Question 44
Let $\triangle ABC$ be an equilateral triangle with the side of $20$ units. Vid divides this triangle into $400$ smaller equilateral triangles with the sides of $1$ unit. Eva then picks $4$ of the vertices of these smaller triangles. The vertices lie inside the triangle $ABC$ and form a parallelogram with sides parallel to the sides of the triangle $ABC$. There are exactly $46$ smaller triangles that have at least one point in common with the sides of this parallelogram. Find all possible values for the area of this parallelogram.
