Area - squares and rectangles

problem
Griddy region

Age

14 to 16

Challenge level

Weekly Problem 34 - 2008
What is the area of the region common to this triangle and square?
problem
Tiling

Age

7 to 11

Challenge level

An investigation that gives you the opportunity to make and justify predictions.
problem
A day with Grandpa

Age

7 to 11

Challenge level

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

Age

7 to 11

Challenge level

What do these two triangles have in common? How are they related?
problem
3x3 areas

Age

11 to 14

Challenge level

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

Age

7 to 11

Challenge level

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.
problem
Proof of Pick's theorem

Age

16 to 18

Challenge level

Follow the hints and prove Pick's Theorem.
problem
Double cover

Age

11 to 14

Challenge level

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

Age

14 to 16

Challenge level

Can you work out the shaded area surrounded by these arcs?
problem
Square in a triangle

Age

11 to 14

Challenge level

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