# Area - July 2006, All Stages

## Problems

### Sizing Them Up

##### Age 5 to 7 Challenge Level:

Can you put these shapes in order of size? Start with the smallest.

### Wallpaper

##### Age 5 to 7 Challenge Level:

These pieces of wallpaper need to be ordered from smallest to largest. Can you find a way to do it?

##### Age 7 to 11 Challenge Level:

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

### Torn Shapes

##### Age 7 to 11 Challenge Level:

These rectangles have been torn. How many squares did each one have inside it before it was ripped?

### More Transformations on a Pegboard

##### Age 7 to 11 Challenge Level:

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

### Cuboid-in-a-box

##### Age 7 to 11 Challenge Level:

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

### All Wrapped Up

##### Age 7 to 11 Challenge Level:

What is the largest cuboid you can wrap in an A3 sheet of paper?

### Squares in Rectangles

##### Age 11 to 14 Challenge Level:

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

### Warmsnug Double Glazing

##### Age 11 to 14 Challenge Level:

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

### Two Shapes & Printer Ink

##### Age 14 to 16 Challenge Level:

If I print this page which shape will require the more yellow ink?

### Trapezium Four

##### Age 14 to 16 Challenge Level:

The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?

### Areas of Parallelograms

##### Age 14 to 16 Challenge Level:

Can you find the area of a parallelogram defined by two vectors?

### Peeling the Apple or the Cone That Lost Its Head

##### Age 14 to 16 Challenge Level:

How much peel does an apple have?

### Integral Equation

##### Age 16 to 18 Challenge Level:

Solve this integral equation.

### Integral Sandwich

##### Age 16 to 18 Challenge Level:

Generalise this inequality involving integrals.

### Integral Inequality

##### Age 16 to 18 Challenge Level:

An inequality involving integrals of squares of functions.