# Problem of the Week Problem D From Square to Hexagon

A square piece of paper, $$PQRS$$, has side length $$40$$ cm. The page is grey on one side and white on the other side. Point $$M$$ is the midpoint of side $$PQ$$ and point $$N$$ is the midpoint of side $$PS$$.

The paper is folded along $$MN$$ so that $$P$$ touches the paper at the point $$P'$$.

Point $$T$$ lies on $$QR$$ and point $$U$$ lies on $$SR$$ such that $$TU$$ is parallel to $$MN$$, and when the paper is folded along $$TU$$, the point $$R$$ touches the paper at the point $$R'$$ on $$MN$$.

What is the area of hexagon $$NMQTUS$$?

Here are some known properties of the diagonals of a square that may be useful:

• the diagonals are equal in length; and

• the diagonals right bisect each other; and

• the diagonals bisect the corner angles.