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8 Methods for Three by One

This problem in geometry has been solved in no less than EIGHT ways by a pair of students. How would you solve it? How many of their solutions can you follow? How are they the same or different? Which do you like best?

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Figure of Eight

On a nine-point pegboard a band is stretched over 4 pegs in a "figure of 8" arrangement. How many different "figure of 8" arrangements can be made ?

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Sine and Cosine for Connected Angles

The length AM can be calculated using trigonometry in two different ways. Create this pair of equivalent calculations for different peg boards, notice a general result, and account for it.

Squ-areas

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

The diagram shows three squares on the sides of a triangle $ABC$.

Their areas are respectively 18 000, 20 000 and 26 000 square centimetres.

If the squares are joined, three more triangular areas are enclosed. What is the area of this convex hexagon?