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### Advanced mathematics

# Perimeter, Area and Volume - Stage 3

### Blue and White

### Isosceles Triangles

### Perimeter Possibilities

### Triangles in a Square

### Can They Be Equal?

### Perimeter Challenge

### Colourful Cube

### Changing Areas, Changing Perimeters

### Fence It

### Isometric Areas

### Changing Areas, Changing Volumes

### More Isometric Areas

### Shear Magic

### On the Edge

### Sending a Parcel

### Cuboid Challenge

### Efficient Cutting

### Cola Can

### Cuboids

### Perimeter, Area and Volume Short Problems

### Triangle in a Trapezium

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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?

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?

Age 11 to 14

Challenge Level

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

Age 11 to 14

Challenge Level

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

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?

Age 11 to 14

Challenge Level

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

Age 11 to 14

Challenge Level

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

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?

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?

Age 11 to 14

Challenge Level

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

Age 11 to 14

Challenge Level

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?

Age 11 to 14

Challenge Level

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

Age 11 to 14

Challenge Level

Explore the area of families of parallelograms and triangles. Can you find rules to work out the areas?

Age 11 to 14

Challenge Level

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

Age 11 to 14

Challenge Level

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

Age 11 to 16

Challenge Level

What's the largest volume of box you can make from a square of paper?

Age 11 to 14

Challenge Level

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.

Age 11 to 14

Challenge Level

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

Age 11 to 14

Challenge Level

Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

Age 11 to 16

A collection of short problems on area and volume.

Age 11 to 16

Challenge Level

Can you find and prove the relationship between the area of a trapezium and the area of a triangle constructed within it?