The diagram shows a triangle \(ABC\). \(D\) is a point on \(AB\) and \(E\) is a point on \(AC\) such that \(DE\) is parallel to \(BC\) and \(DE=10\text{ cm}\).
Show that the triangles \(ADE\) and \(ABC\) are similar. Give a reason for each statement you make.[2]
The ratio area of triangle \(ADE\) : area of triangle \(ABC\) is \(4:25\). If the area of triangle \(ABC\) is \(200\text{ cm}^2\), find the height of the trapezium \(DECB\).[3]
The diagram shows a square, \(ABFG\), a regular pentagon, \(BCDEF\), and two sides of a third regular polygon, \(GF\) and \(FE\).
Find the number of sides for the third regular polygon.[3]