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.

Same Height

Age 14 to 16 Challenge Level:

A trapezium is divided into four triangles by its diagonals.
Suppose the two triangles containing the parallel sides have areas
a and b, what is the area of the trapezium?