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?

We usually use squares to measure area, but what if we use triangles instead?

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?

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

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?

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

A colourful cube is made from little red and yellow cubes. But can you work out how many of each?

Can you maximise the area available to a grazing goat?

How can you change the surface area of a cuboid but keep its volume the same? How can you change the volume but keep the surface area the same?

Isometric Areas explored areas of parallelograms in triangular units. Here we explore areas of triangles...

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

What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?

What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?

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.

Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

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

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?

A collection of short Stage 3 problems on area and volume.