problem
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
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
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
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
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
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
Triangles in a square
Age
11 to 14
Challenge level
What are the possible areas of triangles drawn in a square?
problem
Perimeter challenge
Age
11 to 14
Challenge level
Can you deduce the perimeters of the shapes from the information given?
problem
An unusual shape
Age
11 to 14
Challenge level
Can you maximise the area available to a grazing goat?
problem
On the edge
Age
11 to 14
Challenge level
If you move the tiles around, can you make squares with different coloured edges?
problem
Warmsnug double glazing
Age
14 to 16
Challenge level
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
problem
Pick's theorem
Age
14 to 16
Challenge level
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.