Week 5, Term 2

This week I've done some work on Pythagoras's Theorem.
Pythagoras's theorem says that if you drew a perfect square along each of the lines of a right-angled triangle, the area of the square on the hypotenuse of the triangle is equal to the sum of the areas of the other two triangles.
I know that it doesn't work if you draw semicircles instead of squares, but it does work if you draw iscoceles triangles with a right angle. Or any shape with two equal edges and a right angle. I'm not sure about ones that aren't right-angled.
I had to do an excersise where there was a perfect square inside an perfect circle, and each of the four corners was touching the circle. Each of the sides of the square were ten centimeters long.  The excersise was to find the area of the circle. I figured it was easy, all you had to do was find the diameter, which meant all you had to do was find the length of a straight line that diagonally from corner to corner of the square. So, what I learnt you needed to do, was to apply Pythagoras's theorem. This square was cut in half, so I had a right angled iscoceles triangle. Sides a and b were both ten centimeters long, so the square on those sides were 10 squared, so that was 100 cm + 100 cm = 200cm. Therefore, to find the diameter of the circle, you just had to find the square root of 200, which is  14.14213562 ( that's as far as my calculator goes).