### Tilted Squares

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

### Four or Five

The diagram shows a large rectangle composed of 9 smaller rectangles. If each of these rectangles has integer sides, what could the area of the large rectangle be?

### From One Shape to Another

Read about David Hilbert who proved that any polygon could be cut up into a certain number of pieces that could be put back together to form any other polygon of equal area.

# Framed

##### Age 11 to 14 Challenge Level:

Seven small pictures, all square or rectangular, with sides measuring a whole number of inches and each with a different area, have frames exactly one inch wide.

In each case the area of the frame is either the same as the area of the picture or a multiple of it.

The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches.

Find the dimensions of the pictures, show how they fit together to make a rectangle, and find the width of the rectangle.