Area - squares and rectangles

problem
Diagonal touch

Age

14 to 16

Challenge level

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

Age

14 to 16

Challenge level

Work out the radius of a roll of adhesive tape.
problem
Guillotine

Age

11 to 14

Challenge level

Weekly Problem 9 - 2006
What fraction of the area of the rectangle is shaded?
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?
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
Tangram area

Age

11 to 14

Challenge level

Weekly Problem 29 - 2008
The seven pieces in this 12 cm by 12 cm square make a Tangram set. What is the area of the shaded parallelogram?
problem
Unusual quadrilateral

Age

14 to 16

Challenge level

This quadrilateral has an unusual shape. Are you able to find its area?
problem
Symmetric angles

Age

14 to 16

Challenge level

This diagram has symmetry of order four. Can you use different geometric properties to find a particular length?
problem
11x11 square

Age

11 to 16

Challenge level

Here's a neat trick you can do with an 11 by 11 square...
problem
Framed

Age

11 to 14

Challenge level

Seven small rectangular pictures have one inch wide frames. 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.