Area - squares and rectangles

An investigation that gives you the opportunity to make and justify predictions.

Grandpa was measuring a rug using yards, feet and inches. Can you help William to work out its area?

What do these two triangles have in common? How are they related?

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

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.

Follow the hints and prove Pick's Theorem.

Weekly Problem 3 - 2007
What is the ratio of the area of the table covered twice, to the uncovered area?

Can you work out the shaded area surrounded by these arcs?

Weekly Problem 33 - 2006
A square is inscribed in an isoscles right angled triangle of area $x$. What is the area of the square?

These pieces of wallpaper need to be ordered from smallest to largest. Can you find a way to do it?