h.) How is this result related to area found in part b i.) using the result develop a general formula for the area of a polygon with known verticies j.) Using this equation find the area of a pentagon with the verticies (3,-1) (4,2) (1,6) (-3,4) (-2,-1)
Using greens theorem determine the area of the triangle with the vertices (a,b) (c,d) (e,f)
a.) draw a picture of the triangle with the vertices labled
b.) Using
c.) state greens theorem for this problem
d.) find ∫C1xdy-ydx where C1 is the line connecting (a,b) to (c,d)
e.) find ∫C2xdy-ydx where C2 is the line connecting (c,d) to (e,f)
f.) find ∫C3xdy-ydx where C3 is the line connecting (e,f) to (a,b)
g.) find ∫C1xdy-ydx + ∫C2xdy-ydx + ∫C3xdy-ydx
h.) How is this result related to area found in part b
i.) using the result develop a general formula for the area of a
j.) Using this equation find the area of a pentagon with the verticies (3,-1) (4,2) (1,6) (-3,4) (-2,-1)
Using the answers below please answer parts h, i, and j
(b) A = 1/2 |u x v| = 1/2 |ad + cf + eb - af - cd - be|
(d) ∫C1xdy−ydx=(ad−bc)
(e) ∫C2xdy−ydx=(cf−de)
(f) ∫C3xdy−ydx=(eb−af)
(g) ∫C1xdy−ydx+∫C2xdy−ydx+∫C3xdy−ydx=(ad−bc)+(cf−de)+(eb−af)
Thank you
Step by step
Solved in 3 steps
