## Maple's method to find area of complex shapes

Hello, I'm new to this website i really need help.

Here's my problem.
I have an assignment on finding the area of islands, using 3 methods Simpson's, Maples and Monte Carlo.

I have found the area of the islands no problem, but I'm up to the part where I must explain the strengths and limitations of each method. To do this I've conducted a mini investigation into each method by using a simple shape finding the the actual area then using the each method to calculate the area. As well as changing aspect of each method to get see how it effects the result.

When investigating the Maple's method I used a simple triangle Base = 8 cm, Height = 8 cm thus the Area being 32 cm^2.
I applied maples method making line every 10 degrees, and got 31.99 cm^2 (an expected result).
However when I did maples method with lines at 45 degrees i got an answer of 36.63cm^2.

What i don't get is the how it equals 36.63 cm^2, larger than the 'actual' area 32cm^2, when it you look at this picture is should equal less as the two bottom corners should be cut off???

http://img13.imageshack.us/img13/923...entmaples3.jpg

Thank you. it might be something very simple but its bugging me so much.