to #1:

The shorter diagonal bisect the greater angle. Therefore you are dealing with 4 right triangles with the shorter leg of 3 cm and the longer leg is

.

The area is then

to #2:

A regular hexagon consists of 6 equilateral triangles. If the length of one side of the triangle is a then the height of the triangle is:

Therefore the area of an equilateral triangle is:

And finally the area of a regular hexagon is:

. Plug in the value of a (= 12) to calculate the area.