### Golden Thoughts

Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

### Days and Dates

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

# Unusual Polygon

##### Stage: 4 Short Challenge Level:

The diagram shows a polygon ABCDEFG, in which $FG =6$ and $GA=AB=BC=CD=DE=EF$.

Also $BDFG$ is a square.

The area of the whole polygon is exactly twice the area of $BDFG$.

Find the length of the perimeter of the polygon.

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
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