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Golden Thoughts

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.

From All Corners

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.

Same Height

A trapezium is divided into four triangles by its diagonals. Can you work out the area of the trapezium?

Star Gazing

Age 14 to 16 Challenge Level:

Find the ratio of the outer shaded area to the inner area for a six pointed star and the eight pointed star.