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
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.
We use statistics to give ourselves an informed view on a
subject of interest. This problem explores how to scale countries
on a map to represent characteristics other than land area.
Let's start with a simple example of a three-country continent.
The countries all share a border with each other and together are
surrounded by sea.
One way you might do this is given below - can you improve on
What are the good and bad points about this method?
This map was produced in Word using the Draw menu bar. If you
right-click on an object you can specify the % change in either
direction (look on the "size" tab)