Area - July 2006, All Stages

Problems

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Sizing Them Up

Stage: 1 Challenge Level: Challenge Level:1

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

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Wallpaper

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Brush Loads

Stage: 2 Challenge Level: Challenge Level:1

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.

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Torn Shapes

Stage: 2 Challenge Level: Challenge Level:1

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

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More Transformations on a Pegboard

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Cuboid-in-a-box

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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All Wrapped Up

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Warmsnug Double Glazing

Stage: 3 Challenge Level: Challenge Level:1

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

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Squares in Rectangles

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Two Shapes & Printer Ink

Stage: 4 Challenge Level: Challenge Level:1

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

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Trapezium Four

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Areas of Parallelograms

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Peeling the Apple or the Cone That Lost Its Head

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

How much peel does an apple have?

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Integral Equation

Stage: 5 Challenge Level: Challenge Level:1

Solve this integral equation.

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Integral Sandwich

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Generalise this inequality involving integrals.

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Integral Inequality

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

An inequality involving integrals of squares of functions.