Pythagoras' theorem

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Hex

Age

11 to 14

Challenge level

1 out of 3

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.
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Tilted Squares

Age

11 to 14

Challenge level

1 out of 3

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

Age

11 to 14

Challenge level

2 out of 3

Can you minimise the amount of wood needed to build the roof of my garden shed?
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Pythagoras Proofs

Age

11 to 16

Challenge level

2 out of 3

Can you make sense of these three proofs of Pythagoras' Theorem?
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Where Is the Dot?

Age

14 to 16

Challenge level

1 out of 3

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?
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Generating Triples

Age

14 to 16

Challenge level

1 out of 3

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?
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Three Cubes

Age

14 to 16

Challenge level

2 out of 3

Can you work out the dimensions of the three cubes?
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Zig Zag

Age

14 to 16

Challenge level

2 out of 3

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?
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Semi-Detached

Age

14 to 16

Challenge level

2 out of 3

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.
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Inscribed in a Circle

Age

14 to 16

Challenge level

2 out of 3

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?