Weekly Problem 10 - 2012

If you know how long Meg's shadow is, can you work out how long the shadow is when she stands on her brother's shoulders?

Weekly Problem 13 - 2012

The diagram shows contains some equal lengths. Can you work out one of the angles?

Weekly Problem 21 - 2012

Two rectangles are drawn in a rectangle. What fraction of the rectangle is shaded?

Weekly Problem 50 - 2012

The diagram shows a regular dodecagon. What is the size of the marked angle?

In the figure given in the problem, calculate the length of an edge.

A triangle has been drawn inside this circle. Can you find the length of the chord it forms?

What is the area of the region common to this triangle and square?

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

A garden has the shape of a right-angled triangle. A fence goes from the corner with the right-angle to a point on the opposite side. How long is the fence?

Weekly Problem 8 - 2010

Are you able to find triangles such that these five statements are true?

Weekly Problem 29 - 2010

An isosceles triangle is drawn inside another triangle. Can you work out the length of its base?

Weekly Problem 1 - 2011

Use facts about the angle bisectors of this triangle to work out another internal angle.

How does the perimeter change when we fold this isosceles triangle in half?

Weekly Problem 5 - 2013

The diagram shows 8 shaded squares inside a circle. What is the shaded area?

Weekly Problem 27 - 2014

Four congruent isosceles trapezia are placed in a square. What fraction of the square 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 37 - 2014

Which of the five diagrams below could be drawn without taking the pen off the page and without drawing along a line already drawn?

Weekly Problem 41 - 2014

Three straight lines divide an equilateral triangle into seven regions. What is the side length of the original triangle?

Weekly Problem 15 - 2015

In the diagram, two lines have been draawn in a square. What is the ratio of the areas marked?

Weekly Problem 35 - 2015

The diagram has rotational symmetry of order 4. What is the length BC?

Weekly Problem 12 - 2016

The diagram shows a square PQRS and two equilateral triangles RSU and PST. PQ has length 1. What is the length of TU?

Weekly Problem 39 - 2016

In the diagram, VWX and XYZ are congruent equilateral triangles. What is the size of angle VWY?

Weekly Problem 41 - 2016

The diagram shows a square, with lines drawn from its centre. What is the shaded area?

Weekly Problem 33 - 2017

If the midpoints of the sides of a right angled triangle are joined, what is the perimeter of this new triangle?

Weekly Problem 43 - 2017

The diagram shows a semicircle inscribed in a right angled triangle. What is the radius of the semicircle?