Q:

Multidisciplinary problem

I am looking for ideas for an activity for high school students, which involves plane geometry and another field, such as algebra, series, etc...
For example, in junior high there is a nice activity in which students are investigating the idea of pi, by taking rounded shapes, such as plates, measuring the perimeter and radius of each one of them, then setting an XY Cartesian axes, putting points from the measures and calculating the slope, which is pi (if we take 2r on the x axis).
I am looking for similar activity, has to be geometry, but slightly harder, for high school students. It has to involve algebra or any other field (perhaps apart from Trigonometry because that makes the geometry too easy).
Any ideas will be most appreciated !

A:

Pick's Theorem is a great link between area of polygons and the algebraic skill of writing expressions. Nrich maths has a ready to go investigation of Pick's theorem: https://nrich.maths.org/pickstheorem.
Coordinate geometry and transformations are another area with a huge amount of overlap between geometry and algebra.

