Area - squares and rectangles

What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?

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?

Follow the hints and prove Pick's Theorem.

Weekly Problem 21 - 2012
Two rectangles are drawn in a rectangle. What fraction of the rectangle is shaded?

Have a good look at these images. Can you describe what is happening? There are plenty more images like this on NRICH's Exploring Squares CD.

If I use 12 green tiles to represent my lawn, how many different ways could I arrange them? How many border tiles would I need each time?

If a new and an old television have screens of the same area, what is the ratio of their widths?

Which of the following shaded regions has an area different from the other shaded regions?

What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?

Choose a box and work out the smallest rectangle of paper needed to wrap it so that it is completely covered.