Triangles

The graph below is an oblique coordinate system based on 60 degree angles. It was drawn on isometric paper. What kinds of triangles do these points form?

Weekly Problem 13 - 2012
The diagram shows contains some equal lengths. Can you work out one of the angles?

How can the school caretaker be sure that the tree would miss the school buildings if it fell?

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

Weekly Problem 9 - 2012
What is the angle QPT in this diagram?

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?

What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?

Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?