In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?
Follow the instructions and you can take a rectangle, cut it into 4 pieces, discard two small triangles, put together the remaining two pieces and end up with a rectangle the same size. Try it!
You can move the 4 pieces of the jigsaw and fit them into both outlines. Explain what has happened to the missing one unit of area.
The diagram shows a semi-circle and an isosceles triangle which have equal areas. What is the value of $\tan x^{\circ}$?
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.