Great Squares

Investigate how this pattern of squares continues. You could measure lengths, areas and angles.

Paving the Way

A man paved a square courtyard and then decided that it was too small. He took up the tiles, bought 100 more and used them to pave another square courtyard. How many tiles did he use altogether?

Square Areas

Can you work out the area of the inner square and give an explanation of how you did it?

The Pi Are Square

Stage: 3 Challenge Level:

This problem was a rather special one, because many of you would not have learnt about pi yet at school.

This solution by Rebeccca Jackson (11 years) from the Sum Fun Maths Club (Stamford High School, Lincolnshire) sets out the steps for solving the problem very clearly. Rebecca has used 3.14 for pi, as was suggested in the problem, and has calculated correctly.

Christina Ivanova (London) agreed with this answer

George Vassilev (10 years, Rosebank Primary, Leeds) sent in a well written summary of how he worked out this problem.

"The first thing I did was to find a side of the square = 4.4. I found that by 2.2 x2cm. which is the radius time 2. After that I found out the area of the square: 4.4cm x 4.4cm = 19.36cm 2. Afterwards I found the area of the circle: 4.14 x 2.2 x 2.2 = 15.1976cm 2. Then I subtracted them to find out what area of the square is not covered by the circle: 19.36 - 15.1976 = 4.1624cm 2."

This excellent solution was sent in by Syed Farhan Iskandar, (12 years, Foxford School and Community College). It doesn't actually state what value was used for pi though, but it must have had 10 decimal places. This is why this answer is slightly different to some others.

Process 1: Finding out area of square

Radius of circle x 2 = length and width of each sides of the square

2.2 cm x 2 = 4.4 cm

Length x width = area of square

4.4 cm x 4.4 cm = 19.36 cm 2

Area of square is 19.36 cm 2

Process 2: Finding out area of circle

pr 2 = area of circle

p x 2.2 cm 2 = 15.20530844 cm 2

Area of circle is 15.20530844 cm 2

Process 3: Finding out area of square-not covered by circle

Area of square - area of circle = area of square-not covered by circle

19.36 cm 2 - 15.20530844 cm 2 = 4.15469156 cm 2

Area of square-not covered by circle is 4.15469156 cm 2