Area - squares and rectangles

problem
Through the window

Age

7 to 11

Challenge level

My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?
problem
Making squares

Age

7 to 11

Challenge level

Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?
problem
Fitted

Age

7 to 11

Challenge level

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?
problem
A day with Grandpa

Age

7 to 11

Challenge level

Grandpa was measuring a rug using yards, feet and inches. Can you help William to work out its area?
problem
Extending great squares

Age

7 to 11

Challenge level

Explore one of these five pictures.
problem
Cylinder cutting

Age

7 to 11

Challenge level

An activity for high-attaining learners which involves making a new cylinder from a cardboard tube.
problem
Tiling into slanted rectangles

Age

7 to 11

Challenge level

A follow-up activity to Tiles in the Garden.
problem
Cover the tray

Age

7 to 11

Challenge level

These practical challenges are all about making a 'tray' and covering it with paper.
problem
Ribbon squares

Age

7 to 11

Challenge level

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
article
From one shape to another

Read about David Hilbert who proved that any polygon could be cut up into a certain number of pieces that could be put back together to form any other polygon of equal area.