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A tennis ball is served from directly above the baseline (assume the ball travels in a straight line). What is the minimum height that the ball can be hit at to ensure it lands in the service area?

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If the sides of the triangle in the diagram are 3, 4 and 5, what is the area of the shaded square?

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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.

Triangular Tantaliser

Age 11 to 14 Challenge Level:

Here is a 4 by 4 dotty grid:
Picture of a Geoboard with four rows of four pegs

How many different triangles can you draw by joining dots on the grid?
We count two triangles as the same if you can cut one out and fit it exactly on top of the other.

Can you come up with a convincing argument that you have found all the possible triangles?