Area of triangle = 1/2 x base x heightFor your sector, you have:
base = r
height = r sin(a) [Where 'a' is the included angle]
Therfore, the triangle area is:
1/2 x r x r sin(a) = r2/2(sin(a))The area of the entire sector is the proportion that the sector constitutes of the area of the circle, i.e.:
a/2π x πr2 = ar2/2a/2π gives the proportion of the circle occupied by the sector
πr2 obviously gives the area of the entire circle
Therefore, the area of the sector minus the area of the triangle is:
(ar2/2) - (r2/2(sin(a)))We can take out a factor of r
2/2 giving:
r2/2(a - sin(a))Now, the only quantities we require from the polyline arc is the included angle & the arc radius.
The polyarc bulge is the tangent of 1/4 of the included angle, therefore, the inverse of this operation gives the included angle from the bulge value:
a = 4 x atan(b)As for the bulge radius, there are various ways to acquire this value - here is one example:
;; Bulge Radius - Lee Mac
;; p1 - start vertex
;; p2 - end vertex
;; b - bulge
;; Returns the radius of the arc described by the given bulge and vertices
(defun LM:BulgeRadius
( p1 p2 b
) )
Now you have all the tools & information you require to calculate the required area