Triangle Midpoints
Age 14 to 16
Challenge Level
You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?
Blue and White
Age 11 to 14
Challenge Level
Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?
Arclets
Age 14 to 16
Challenge Level
Each of the following shapes is made from arcs of a circle of radius r. What is the perimeter of a shape with 3, 4, 5 and n "nodes".
Marbles in a Box
Age 11 to 16
Challenge Level
How many winning lines can you make in a three-dimensional version of noughts and crosses?
Hexy-metry
Age 14 to 16
Challenge Level
A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?
Three by One
Age 16 to 18
Challenge Level
There are many different methods to solve this geometrical problem - how many can you find?
Triangles and Petals
Age 14 to 16
Challenge Level
An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?
Tilted Squares
Age 11 to 14
Challenge Level
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
On the Edge
Age 11 to 14
Challenge Level
If you move the tiles around, can you make squares with different coloured edges?
Sending a Parcel
Age 11 to 14
Challenge Level
What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?
Where to Land
Age 14 to 16
Challenge Level
Chris is enjoying a swim but needs to get back for lunch. How far along the bank should she land?
Square Coordinates
Age 11 to 14
Challenge Level
A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?
Right Angles
Age 11 to 14
Challenge Level
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
Semi-regular Tessellations
Age 11 to 16
Challenge Level
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
Trapezium Four
Age 14 to 16
Challenge Level
The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?
Cola Can
Age 11 to 14
Challenge Level
An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?
Can They Be Equal?
Age 11 to 14
Challenge Level
Can you find rectangles where the value of the area is the same as the value of the perimeter?
Cuboid Challenge
Age 11 to 16
Challenge Level
What's the largest volume of box you can make from a square of paper?
Curvy Areas
Age 14 to 16
Challenge Level
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
Circles in Quadrilaterals
Age 14 to 16
Challenge Level
Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.
Which Solids Can We Make?
Age 11 to 14
Challenge Level
Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?
Opposite Vertices
Age 11 to 14
Challenge Level
Can you recreate squares and rhombuses if you are only given a side or a diagonal?
Fit for Photocopying
Age 14 to 16
Challenge Level
Explore the relationships between different paper sizes.
Vector Journeys
Age 14 to 18
Challenge Level
Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?
Perimeter Possibilities
Age 11 to 14
Challenge Level
I'm thinking of a rectangle with an area of 24. What could its perimeter be?
NRICH is part of the family of activities in the Millennium Mathematics Project.