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Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

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Square Areas

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

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Kissing Triangles

Determine the total shaded area of the 'kissing triangles'.

Dividing a Square

Age 11 to 14 Short Challenge Level:
Three lines have been drawn from the centre of this square to split it into two congruent trapezia and a pentagon.

The side length of the square is 1, and the areas of the three shapes are all equal.

What is the length $x$?

This problem is adapted from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.