Blue and white
Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?
Fence it
Isosceles triangles
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?
Can they be equal?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
Changing areas, changing perimeters
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?
Perimeter possibilities
I'm thinking of a rectangle with an area of 24. What could its perimeter be?
Triangles in a square
What are the possible areas of triangles drawn in a square?
Perimeter challenge
Can you deduce the perimeters of the shapes from the information given?
An unusual shape
Can you maximise the area available to a grazing goat?
On the edge
If you move the tiles around, can you make squares with different coloured edges?
Warmsnug double glazing
Pick's theorem
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.