module Shape (Shape(Rectangle,Ellipse,RtTriangle,Polygon),
 Radius,Side,Coordinate,Vertex,square,circle,
 distBetween,area) where
type Radius = Float
type Side = Float
type Coordinate = (Float,Float)
type Vertex = Coordinate
data Shape = Rectangle Side Side
 | Ellipse Radius Radius
 | RtTriangle Side Side
 | Polygon [ Coordinate ]
 deriving Show
circle radius = Ellipse radius radius
square side = Rectangle side side
area :: Shape -> Float
area (Rectangle s1 s2) = s1 * s2
area (Ellipse r1 r2) = pi * r1 * r2
area (RtTriangle s1 s2) = (s1 *s2) / 2
area (Polygon (v1:pts)) = polyArea pts
 where polyArea :: [ (Float,Float) ] -> Float
 polyArea (v2 : v3 : vs) = triArea v1 v2 v3 +
 polyArea (v3:vs)
 polyArea _ = 0
 
triArea v1 v2 v3 = 
 let a = distBetween v1 v2
 b = distBetween v2 v3
 c = distBetween v3 v1
 s = 0.5*(a+b+c)
 in sqrt (s*(s-a)*(s-b)*(s-c))
 
 
distBetween (x1,y1) (x2,y2) 
 = sqrt ((x1-x2)^2 + (y1-y2)^2) 
 
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