### Doesn't Add Up

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:

Let the radius of the circle be r and let the perpendicular height of the triangle be h.

$\tan x^{\circ}= h/r$

Now, the area of the semicircle = ${1\over2}\pi r^2$ and the area of the triangle = ${1\over2}\times 2r \times h$

Which gives $r h$ = ${1\over2}\pi r^2$, so ${h\over r} = {\pi \over 2}$

This problem is taken from the UKMT Mathematical Challenges.

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