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?

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

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?

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?

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

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 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?

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?

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

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?

Find the shaded area of these shapes with perimeters made of semicircles.

What fraction of the larger circle is outside the smaller circle?

Weekly Problem 9 - 2006

What fraction of the area of the rectangle is shaded?

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 3 - 2009

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

Weekly Problem 17 - 2015

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

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

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?