### Kissing Triangles

Determine the total shaded area of the 'kissing triangles'.

### Trice

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?

### Linkage

Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?

# Hex

##### Stage: 3 Challenge Level:
If the original hexagon has sides of length 3 units what is the length of the sides of the smaller hexagons?