# Exercise 2.5

```{-
Area of a shape: compute by adding up the trapezoidal areas
formed by pair of vertices with the x-axis.
This can (correctly) be negative when x2 > x1.
-}

axisTrapezoidArea :: Vertex -> Vertex -> Float
axisTrapezoidArea (x1, y1) (x2, y2) = (x1 - x2) * (y1 + y2) * 0.5

area :: Shape -> Float
area (Polygon (v1:vs)) = polyArea v1 vs
where polyArea v (vnext:vs') = axisTrapezoidArea v vnext
+ polyArea vnext vs'
polyArea vlast [] = axisTrapezoidArea vlast v1```

Wrapping the head of a list in this way is more idiomatically done with

`list ++ [head list]`

rather than pattern matching the end of the list. However, at this stage in the book, we’re Haskell newbies.

### 4 responses to “Exercise 2.5”

1. fero says:

It’s not working! Try area (Polygon [(7,0),(4,0),(4,5),(0,5)]) -> 2.5 but should be 17.5 (with triangle solution from book)

2. fero says:

Actually I don’t know how to solve it. I have almos the same solution, I found that it is wrong so I am in search of correct one:)

3. admin says:

Fero, your Polygon [(7,0),(4,0),(4,5),(0,5)] is self-crossing. This algorithm is inadequate for self-crossing polygons, but it is correct for concave polygons.

4. fero says:

Thanks Ben, you are right. When I swap last two vertexes – area (Polygon [(7,0),(4,0),(0,5),(4,5)]) , it will not be a self-crossing polygon and it works as expected.