Question

1.
A) 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.

b) A rectangular piece of paper, PQRS, has PQ = 30 cm and P S = 40 cm. The paper has grey lines on one side and is plain white on the other. The paper is folded so that the two diagonally opposite corners P and R coincide.
This creates a crease along line segment AC, with A on PS and C on QR.
Determine the length of AC.

This question can be found at Waterloo problem of the week A = Grade 9/10
B = Grade 11/12