Midpoint polygon

It shares the same centroid and medians with the original triangle.

The perimeter of the medial triangle equals the semiperimeter of the original triangle, and the area is one quarter of the area of the original triangle.

This can be proven by the midpoint theorem of triangles and Heron's formula.

If the quadrilateral is simple, the area of the parallelogram is one half the area of the original quadrilateral.

The perimeter of the parallelogram equals the sum of the diagonals of the original quadrilateral.