PART 1:
First I worked out the middle beams length using the birds eye view, I added the 2 Red lengths of 120 to make 240, then I subtracted this from 300cm. This left me 60cm as the length of the middle beam.
To work out the length of the sloping beams. I needed to create a right angled triangle with the sloping beam as the hypotenuse. I know that the height of that triangle is 60cm so I needed to work out the length of the triangle base.
I calculated that using the base as the hypotenuse of another right angled triangle I created. I knew from the plan the 2 sides of the new triangle were both 120cm and I used Pythagoras's theorem to calculate that the hypotenuse was 169.7cm.
Returning to the first triangle, I used the height of 60cm and the base of 169.7cm, so, using Pythagoras's theorem I was able to calculate the length of the sloping beam at 180cm. This was the same for all sloping beams.
So the overall amount of wood needed is 4x180cm added to 60cm to total 780cm.
ANSWER: 780cm
PART 2:
To reduce the amount of wood needed we need to make the lengths marked in red smaller; This will make the middle beam larger but will make the sloping beams, of which there are more, smaller. Therefore resulting in less wood being used; For example:
If the red length was 100cm the middle beam would be 100 also, we can tell this using the birds eye view.
Then, using the same technique as PART A with triangles and Pythagoras's theorem I discovered the sloping beams are 167.3cm.
So a roof with red length 100cm would require (4x167.3+100=)769.2cm of wood; 10.8cm less than that needed for a roof with red length 120cm