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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'.

Scalene Area

Age 11 to 14 Short Challenge Level:

The diagram shows a scalene triangle with side lengths 13 cm, 21 cm and 20 cm.

From a point O inside the triangle, line segments can be drawn at right angles to each of the sides.

The lengths of these line segments are 9 cm, 3 cm and 3.6 cm, as shown in the diagram.

What is the area of the triangle?

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