Can you make a tetrahedron whose faces all have the same perimeter?
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?
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
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.