Weekly Problem 33 - 2016

In the diagram, six circles of equal size touch adjacent circles and the sides of the large rectangle. What is the perimeter of the large rectangle?

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 43 - 2016

In the diagram, the small squares are all the same size. What fraction of the large square is shaded?

Weekly Problem 24 - 2007

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

Can you find the volume of a cuboid, given the areas of its faces?

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 50 - 2016

A large cuboid is made from cubes of equal size. What fraction of the surface area of the large cuboid is black?

Weekly Problem 39 - 2013

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

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 20 - 2017

The diagram shows a design formed by drawing six lines in a regular hexagon. What fraction of the hexagon is shaded?

Weekly Problem 23 - 2016

If the area of a face of a cuboid is one quarter of the area of each of the other two visible faces, what is the area of these faces?

Weekly Problem 17 - 2017

Yasmin lengthened one side of her pea bed by 3m to make it a square. This reduced her strawberry patch by $15m^2$. What was the original area of her pea bed?

How many cubes would be visible in a 12 by 12 by 12 Rubik’s cube?

Weekly Problem 23 - 2017

Three small equilateral triangles of the same size are cut from the corners of a larger equilateral triangle. What is the side length of the small triangles?

A square is divided into three shapes which all have equal areas. Can you find the length of this side?

Weekly Problem 49 - 2014

A blue cube is cut into 27 smaller cubes of equal size. What fraction of the total surface area of these cubes is blue?

Weekly Problem 31 - 2017

The triangle HIJ has the same area as the square FGHI. What is the distance from J to the line extended through F and G?

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?

Weekly Problem 35 - 2016

What is the total perimeter of the squares, if the line GH in the diagram is 24cm?

Weekly Problem 3 - 2007

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

Weekly Problem 52 - 2017

Sue cuts some squares from a piece of paper to make a Christmas decoration. What is the perimeter of the resulting shape?

Weekly Problem 27 - 2009

The perimeter of a large triangle is 24 cm. What is the total length of the black lines used to draw the figure?

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?

Can you find the height of the water in this tilted tank when it is flat?

Weekly Problem 32 - 2014

Three overlapping squares are shown. If you know the areas of the overlapping and non-overlapping parts, can you work out the side lengths of the squares?

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 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 28 - 2006

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

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 3 - 2009

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

Draw another line through the centre of this rectangle to split it into 4 pieces of equal area.

Weekly Problem 17 - 2015

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

Weekly Problem 38 - 2015

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

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?