A white cross is placed symmetrically in a red disc with the central square of side length sqrt 2 and the arms of the cross of length 1 unit. What is the area of the disc still showing?
Wedge on Wedge
Stage: 4 Challenge Level:
This problem, based on a structure that includes a compound angle,
could be a standard post-16 trigonometry question, but offered
here, with side lengths selected to make ratio calculations easy,
we hope to encourage students to explore the construction on which
the compound angle formulae rest.
The numbers were chosen to make calculation as easy as possible. It
seemed that once students reached for a calculator to help them
multiply or divide, they would think that the SIN, COS or TAN
buttons were the answer here and this is not a terribly useful
directon to take.
But there may be value in asking students how they might solve the
problem with numbers that they make up for themselves (or for each
other). Can they describe ageneral strategy? It is also useful at
this point to ask whether all the side length data is
A short distance beyond Stage 4 students will have a range of
formulae to apply to problems like this, our aim at this stage is
to help them spend some time exploring the constructions that make
those formulae possible or valid.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.