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30-60-90 Polypuzzle

Stage: 5 Challenge Level: Challenge Level:1

Finding the lengths depends on using the ratio for the sides of a 30-60-90 triangle as the name of the problem suggests. Below the diagrams show how to take the pieces which make a square of unit area and fit the pieces together to make an equilateral triangle of the same area with side $2t$ and knowing this you can calculate $t$. The way pieces fit together gives you that $p=t$ and the rest is up to you!

You can calculate the length '$t$' knowing the area of the equilateral triangle. Pythagoras theorem and the sine rule can be used in finding the other lengths.