Problems
For a natural number \(n\) consider a regular \(2n\)-gon, with every vertex coloured either blue or green. It is known that the number of blue vertices equals the number of green vertices. Show that the number of main diagonals (passing through the centre of the \(2n\)-gon) with both ends blue is the same as the number of main diagonals with both ends green.
Each number denotes the area of a rectangle it is written into. What is the area of the last rectangle?
Divide the trapezium into two parts such that they can be reassembled to make a triangle
In a square \(ABHI\) two smaller squares are drawn: \(ACFG\) with area equal to \(16\) and \(BCED\) with area equal to \(4\). Find the area of hexagon \(DEFGIH\).
If each of the small squares has an area of \(1\), what is the area of the triangle?
Divide the parallelogram into two parts such that they can be reassembled to make a triangle.
Cut a triangle into three parts, which can be reassembled into a rectangle.
On the diagram each number denotes the area of a rectangle it is written into. What are the areas of the other rectangles?
