Pythagoras' theorem

problem
Pythagoras proofs

Age

11 to 16

Challenge level

Can you make sense of these three proofs of Pythagoras' Theorem?
problem
Garden shed

Age

11 to 14

Challenge level

Can you minimise the amount of wood needed to build the roof of my garden shed?
problem
Kite in a square

Age

14 to 18

Challenge level

Can you make sense of the three methods to work out what fraction of the total area is shaded?
problem
Generating triples

Age

14 to 16

Challenge level

Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?
problem
Unusual polygon

Age

14 to 16

Challenge level

What is the perimeter of this unusually shaped polygon...
problem
Folding in half

Age

14 to 16

Challenge level

How does the perimeter change when we fold this isosceles triangle in half?
problem
Centre square

Age

14 to 16

Challenge level

What does Pythagoras' Theorem tell you about the radius of these circles?
problem
Tetromino diagonal

Age

14 to 16

Challenge level

Can you calculate the length of this diagonal line?
problem
Partly circles

Age

14 to 16

Challenge level

What is the same and what is different about these circle questions? What connections can you make?
problem
Rectangle dissection

Age

11 to 14

Challenge level

Weekly Problem 2 - 2009
The 16 by 9 rectangle is cut as shown. Rearrange the pieces to form a square. What is the perimeter of the square?