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In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?

### Lying and Cheating

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!

### Muggles Magic

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.

# Weekly Problem 28 - 2008

##### Stage: 3 and 4 Challenge Level:

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.

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