Problems
Suppose you only knew the area formula of a triangle for right-angled triangles. That is, if a base with length \(b\) and a height \(h\) of a triangle meet at a right angle, you know that the area of the triangle is \(\frac{1}{2}bh\). Can you prove the usual area formula for a general triangle?
There is a pair of parallel lines. The point \(A\) and \(B\) lie on one of the lines. The point \(C\) and \(D\) lies on the other line. We can form triangles \(\triangle ABC\) and \(\triangle ABD\). Prove that the areas of triangles \(\triangle ABC\) and \(\triangle ABD\) are equal.
Let \(ABCDEF\) be a regular hexagon. Points \(G\) and \(H\) lie on \(EF\) and \(DE\) respectively such that \(|EG|=|EH|\). Furthermore, the area of quadrilateral \(ABGF\) is equal to the area of quadrilateral \(BGEH\), which are both equal to the area of \(BCDH\). What’s the ratio \(\frac{|EG|}{|EF|}\)?
In the diagram, all the small squares are of the same size. What fraction of the large square is shaded?
Lines \(AB\) and \(CDE\) are parallel. Which triangle out of \(\triangle ABC\), \(\triangle ABD\) and \(\triangle ABE\) has the greatest area?
