Compute polygon and chess problems

*Must be done in 24 hrs* Problem 1: ---------- Implement the function computePolygonArea :: [(Double,Double)] -> Double that computes the area of the polygon. The formula for the area of the polygon is given at: [login to view URL] You should report an error when the list is empty or contains only one point. You should implement the function det :: (Double,Double) -> (Double,Double) -> Double that computes the determinate of the 2 x 2 matrix whose columns are given by the first and second arguments, respectively. You should use the det function in your computation of the polygon area. Problem 2: ---------- See [login to view URL] for more details Recall we only consider the situation where there is only a single piece on the board Given the definitions --------------------------------------------------------------- type File = Char -- column index -- valid files are 'a','b',...,'h' type Rank = Int -- row index -- valid ranks are 1,2,...8 type Position = (File,Rank) data Color = Black | White deriving (Eq,Show) data Piece = King | Queen | Rook | Bishop | Knight | Pawn deriving (Eq,Show) --------------------------------------------------------------- implement the functions --------------------------------------------------------------- isLegalPosition :: Position -> Bool isLegalMove :: Color -> Piece -> Position -> Position -> Bool --------------------------------------------------------------- that check whether a position is a legal board position and whether a move is legal.