Weekly Problem 24 - 2007

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

Weekly Problem 30 - 2009

M is the midpoint of the side of the rectangle. What is the area (in square units) of the triangle PMR?

Weekly Problem 27 - 2012

Television screens have changed from the traditional 4:3 to widescreen 16:9. If a new television and an old television have the same area, what is the ratio of their widths?

Weekly Problem 50 - 2009

Tom and Jerry start with identical sheets of paper. Each one cuts his sheet in a different way. Can you find the perimeter of the original sheet?

Weekly Problem 39 - 2013

Which of the areas shown in the hexagons are equal to each other?

Weekly Problem 25 - 2010

These four touching circles have another circle hiding amongst them...

Weekly Problem 28 - 2006

What can you say about the rectangles that form this L-shape?

Weekly Problem 23 - 2016

The diagram shows a cuboid in which the area of the shaded face is one quarter of the area of each of the two visible unshaded faces. What is the area of one of the unshaded faces?

Weekly Problem 26 - 2016

A cube has each of its faces covered by one face of an identical cube, making a solid as shown. What is the surface area of the solid?

Weekly Problem 33 - 2014

A rectangle with area $125\text{cm}^2$ has sides in the ratio $4:5$. What is the perimeter of the rectangle?

Weekly Problem 33 - 2006

A square is inscribed in an isoscles right angled triangle of area $x$. What is the area of the square?

Weekly Problem 3 - 2009

What fraction of the area of this regular hexagon is the shaded triangle?

Weekly Problem 49 - 2010

When I place a triangle over a small square, or cover a larger square with the same triangle, a certain proportion of each is covered. What is the area of the triangle?

Weekly Problem 38 - 2011

Given three concentric circles, shade in the annulus formed by the smaller two. What percentage of the larger circle is now shaded?

Weekly Problem 52 - 2006

A square is divided into four rectangles and a square. Can you work out the ratio of the side lengths of the rectangles?

Weekly Problem 9 - 2015

How many triangles can Jack draw with two sides of lengths $6$cm and $8$cm and an area of $7$cm$^2$?

Weekly Problem 52 - 2011

Draw two intersecting rectangles on a sheet of paper. How many regions are enclosed? Can you find the largest number of regions possible?

Weekly Problem 3 - 2007

What is the ratio of the area of the table covered twice to the uncovered area?

Weekly Problem 17 - 2015

A square contains two overlapping squares. What is the total of the shaded regions?

Weekly Problem 37 - 2015

A piece of card is folded to make an open box. Given its surface area, can you work out its volume?

Weekly Problem 30 - 2007

Three-quarters of the area of the rectangle has been shaded. What is the length of x?

Weekly Problem 9 - 2006

What fraction of the area of the rectangle is shaded?

Weekly Problem 37 - 2007

This regular hexagon has been divided into four trapezia and one hexagon.... what is the ratio of the lengths of sides p, q and r?

Weekly Problem 11 - 2016

Four cubes are placed together to make a cuboid. What is the surface area of this cuboid?

Weekly Problem 16 - 2008

A 30cm x 40cm page of a book includes a 2cm margin on each side... What percentage of the page is occupied by the margins?

Weekly Problem 49 - 2014

A solid wooden cube is painted blue on the outside. The cube is then cut into 27 smaller cubes of equal size. What fraction of the total surface area of these new cubes is blue?

Weekly Problem 38 - 2015

Where does the line through P that halves the figure shown meet the edge XY?