why a square with the same area as the parallelogram and with its vertices at the intersection of grid lines cannot be drawn

Question

why a square with the same area as the parallelogram and with its vertices at the intersection of grid lines cannot be drawn

Answer 1

It is not possible to draw a square with the same area as a given parallelogram, both with vertices at the intersection of grid lines, because the sides of the parallelogram are slanted while the sides of a square are perpendicular to each other.

When a parallelogram is drawn on a grid, its sides are not perpendicular to the grid lines. This means that the length of the parallelogram's sides cannot be measured directly from the grid lines. On the other hand, a square has sides that are perpendicular to the grid lines, and the length of its sides can be measured directly from the grid lines.

Thus, it is not possible to draw a square that has the same area as a parallelogram with vertices at the intersection of grid lines because the lengths of the sides of the parallelogram are not the same as the lengths of the sides of a square. While it may be possible to draw a square with the same area as the parallelogram, it would not have its vertices at the intersection of grid lines.