Perimeter and Area

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

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 you find rectangles where the value of the area is the same as the value of the perimeter?

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?

I'm thinking of a rectangle with an area of 24. What could its perimeter be?

What are the possible areas of triangles drawn in a square?

Can you deduce the perimeters of the shapes from the information given?

Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?

Can you maximise the area available to a grazing goat?

If you move the tiles around, can you make squares with different coloured edges?

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

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.