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 out.
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?
Triangle ABC is right angled at A and semi circles are drawn on all three sides producing two 'crescents'.
Show that the sum of the areas of the two crescents equals the area of triangle ABC.