Question: (a) Let D be a polygon in R? and let its vertices in anticlockwise order be (x1, y1), (X2, Y2), ..., (Xn, Yn). Use

(a) Let D be a polygon in R? and let its vertices

(a) Let D be a polygon in R? and let its vertices in anticlockwise order be (x1, y1), (X2, Y2), ..., (Xn, Yn). Use Green's theorem to prove that the area of D is given by the formula 1 5 [(x142 X2y1)+ (x2y3 - X3y2) +.+ (Xn-1Yn - XnYn-1) + (Xny1 - x1yn)]. 2 (b) Use the formula from part (a) to derive the area of a parallelogram with baseb and height h.

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