
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?



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?


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.