This is part of our Secondary Curriculum collection of favourite rich tasks arranged by topic.
Scroll down to see the complete collection, or explore our subcollections on Perimeter and Area in two dimensions, and Surface Area and Volume in three dimensions.
problem
Favourite
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?
problem
Favourite
Perimeter Possibilities
Age
11 to 14
Challenge level
I'm thinking of a rectangle with an area of 24. What could its perimeter be?
problem
Favourite
Triangles in a Square
Age
11 to 14
Challenge level
What are the possible areas of triangles drawn in a square?
problem
Favourite
Perimeter Challenge
Age
11 to 14
Challenge level
Can you deduce the perimeters of the shapes from the information given?
problem
Favourite
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?
problem
Favourite
Isometric Areas
Age
11 to 14
Challenge level
We usually use squares to measure area, but what if we use triangles instead?
problem
Favourite
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?
problem
Favourite
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?
problem
Favourite
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?
problem
Isosceles Triangles Poster
Age
11 to 14
Challenge level
Isosceles Triangles Poster - February 2005
problem
Favourite
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?
problem
Favourite
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?
problem
Favourite
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?
problem
Favourite
More Isometric Areas
Age
11 to 14
Challenge level
Isometric Areas explored areas of parallelograms in triangular units. Here we explore areas of triangles...
problem
Favourite
An Unusual Shape
Age
11 to 14
Challenge level
Can you maximise the area available to a grazing goat?
problem
Favourite
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?
problem
Favourite
On the Edge
Age
11 to 14
Challenge level
If you move the tiles around, can you make squares with different coloured edges?
problem
Favourite
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?
problem
Favourite
Cuboid Challenge
Age
11 to 16
Challenge level
What's the largest volume of box you can make from a square of paper?
problem
Favourite
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?
problem
Favourite
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.
problem
Favourite
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?
Scroll down to see the complete collection, or explore our subcollections on Perimeter and Area in two dimensions, and Surface Area and Volume in three dimensions.
list
Perimeter and Area
Age
11 to 14
Challenge level
This selection of problems is designed to help you teach Perimeter and Area.
list
Surface Area and Volume
Age
11 to 14
Challenge level
This selection of problems is designed to help you teach Surface Area and Volume.
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You may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.