Triangles in a Square
Age 11 to 14
Challenge Level
What are the possible areas of triangles drawn in a square?
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?
Fence It
Age 11 to 14
Challenge Level
This problem challenges students to work systematically while applying their knowledge of areas of rectangles.
Isosceles Triangles
Age 11 to 14
Challenge Level
This problem encourages students to use coordinates, area and isosceles triangles to solve a non-standard problem. To find all possible solutions they will need to work systematically.
Changing Areas, Changing Perimeters
Age 11 to 14
Challenge Level
Working on this problem will give students a deeper understanding of area and perimeter, and how they change as a shape is altered.
Perimeter Challenge
Age 11 to 14
Challenge Level
Can you deduce the perimeters of the shapes from the information given?
Perimeter Possibilities
Age 11 to 14
Challenge Level
This problem combines both area and perimeter by inviting students to consider the different possibilities for the perimeter when the area of a rectangle is fixed.
Can They Be Equal?
Age 11 to 14
Challenge Level
Sometimes area and perimeter of rectangles are taught separately, and are often confused. In this problem students consider the relationship between them.
On the Edge
Age 11 to 14
Challenge Level
If you move the tiles around, can you make squares with different coloured edges?
An Unusual Shape
Age 11 to 14
Challenge Level
This problem offers the opportunity to practise calculating areas of circles and fractions of a circle in the context of an optimisation task.
Warmsnug Double Glazing
Age 14 to 16
Challenge Level
This problem offers students a chance to develop strategies for organising and understanding mixed up information within the context of calculating areas and perimeters of rectangles.
Pick's Theoremlive
Age 14 to 16
Challenge Level
This problem allows students to consolidate their understanding of how to calculate the area of irregular shapes, while offering an opportunity to explore and discover an interesting result.
NRICH is part of the family of activities in the Millennium Mathematics Project.