Pythagoras' theorem

problem
Favourite

Hex

Age

11 to 14

Challenge level

Explain how the thirteen pieces making up the regular hexagon shown in the diagram can be re-assembled to form three smaller regular hexagons congruent to each other.
problem
Favourite

Tilted Squares

Age

11 to 14

Challenge level

It's easy to work out the areas of most squares that we meet, but what if they were tilted?
problem
Favourite

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
Favourite

Pythagoras Proofs

Age

11 to 16

Challenge level

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

Where Is the Dot?

Age

14 to 16

Challenge level

A dot starts at the point (1,0) and turns anticlockwise. Can you estimate the height of the dot after it has turned through 45 degrees? Can you calculate its height?
problem
Favourite

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
Favourite

Three Cubes

Age

14 to 16

Challenge level

Can you work out the dimensions of the three cubes?
problem
Favourite

Zig Zag

Age

14 to 16

Challenge level

Four identical right angled triangles are drawn on the sides of a square. Two face out, two face in. Why do the four vertices marked with dots lie on one line?
problem
Favourite

Semi-Detached

Age

14 to 16

Challenge level

A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.
problem
Favourite

Inscribed in a Circle

Age

14 to 16

Challenge level

The area of a square inscribed in a circle with a unit radius is 2. What is the area of these other regular polygons inscribed in a circle with a unit radius?