maths fencing probWatch
Area of triangle = ½ base length x height. ??????
if this is coursework, then you'll get more marks by showing how you worked out your formula, rather than just making it appear out of nowhere.
for example, for a pentagon, try splitting it up into 5 isosceles triangles and work out the area on one of those triangles. then do the same with hexagons, heptagons and so on... you'll see a pattern begin to emerge, and from that you can get a formula.
by 'set length 1000m' do you mean perimeter or side length? if it's perimeter then you'll need to divide 1000 by the number of sides to get the side length, and you can use that to work out the area of the little triangles using A = 1/2*base*height.
my gcse maths coursework is long gone so i don't know what the general formula is but if you're still stuck i'll try to find it out for you.
meanwhile, try the triangle method and see how it goes!
it's a similar situation to your problem (perimeter = 1000m), and it has all the working out. but if you just want the formula, it's...
A = -----------------
... where n is the number of sides
i think you'd better check to see if it works first.
A = (500)^2 / n.tan(pi/n)
sorry about that!