A point P is selected anywhere inside an equilateral triangle. What
can you say about the sum of the perpendicular distances from P to
the sides of the triangle? Can you prove your conjecture?
What is the area of the quadrilateral APOQ? Working on the building
blocks will give you some insights that may help you to work it
Six circular discs are packed in different-shaped boxes so that the
discs touch their neighbours and the sides of the box. Can you put
the boxes in order according to the areas of their bases?
Have you made a number of different trapezia and found the area of each of the four triangles? (Dynamic geometry software may be useful here)
What did you find?
What are the cases to be considered in the problem? [all four areas different, two matching, three matching, and all four equal] How would the trapezium have to be to make each case occur?