Age 11 to 14
Challenge Level
Perimeter and Area
This selection of problems is a great starting point for learning about Perimeter and Area.
Age 11 to 14
Challenge Level
Surface Area and Volume
This selection of problems is a great starting point for learning about Surface Area and Volume
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?
Cuboids
Age 11 to 14
Challenge Level
Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
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?
Fence It
Age 11 to 14
Challenge Level
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Efficient Cutting
Age 11 to 14
Challenge Level
Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.
Isosceles Triangles
Age 11 to 14
Challenge Level
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
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?
Changing Areas, Changing Perimeters
Age 11 to 14
Challenge Level
How can you change the area of a shape but keep its perimeter the same? How can you change the perimeter but keep the area the same?
Changing Areas, Changing Volumes
Age 11 to 14
Challenge Level
How can you change the surface area of a cuboid but keep its volume the same? How can you change the volume but keep the surface area the same?
Perimeter Possibilities
Age 11 to 14
Challenge Level
I'm thinking of a rectangle with an area of 24. What could its perimeter be?
Triangles in a Square
Age 11 to 14
Challenge Level
What are the possible areas of triangles drawn in a square?
Perimeter Challenge
Age 11 to 14
Challenge Level
Can you deduce the perimeters of the shapes from the information given?
Colourful Cube
Age 11 to 14
Challenge Level
A colourful cube is made from little red and yellow cubes. But can you work out how many of each?
Isometric Areas
Age 11 to 14
Challenge Level
We usually use squares to measure area, but what if we use triangles instead?
More Isometric Areas
Age 11 to 14
Challenge Level
Isometric Areas explored areas of parallelograms in triangular units. Here we explore areas of triangles...
Perimeter, Area and Volume Short Problems
Age 11 to 16
A collection of short problems on area and volume.
Shear Magic
Age 11 to 14
Challenge Level
Explore the area of families of parallelograms and triangles. Can you find rules to work out the areas?
Triangle in a Trapezium
Age 11 to 16
Challenge Level
Can you find and prove the relationship between the area of a trapezium and the area of a triangle constructed within it?
NRICH is part of the family of activities in the Millennium Mathematics Project.