Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.
Straight lines are drawn from each corner of a square to the mid points of the opposite sides. Express the area of the octagon that is formed at the centre as a fraction of the area of the square.
Find the ratio of the outer shaded area to the inner area for a six pointed star and an eight pointed star.
Hint : What fraction is 2/3 of 2/3 of 2/3 . . . twelve times ?
And you've had to double 7 times, so what's the fraction now?
Maybe work in decimals and give the error as a percentage.