Triangles

Move four sticks so there are exactly four triangles.

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

Take it in turns to make a triangle on the pegboard. Can you block your opponent?

If the yellow equilateral triangle is taken as the unit for area, what size is the hole ?

Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?

Prove that a triangle with sides of length 5, 5 and 6 has the same area as a triangle with sides of length 5, 5 and 8. Find other pairs of non-congruent isosceles triangles which have equal areas.

Find all the different shapes that can be made by joining five equilateral triangles edge to edge.

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?

A very mathematical light - what can you see?

ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP : PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED. What is the area of the triangle PQR?