SOLUTION: Find the area of polygon ABCD if the coordinates of the vertices are A(5,-1), B(9,2), C(9,9), and D(0,5).

Algebra ->  Polygons -> SOLUTION: Find the area of polygon ABCD if the coordinates of the vertices are A(5,-1), B(9,2), C(9,9), and D(0,5).      Log On


   

Question 414390: Find the area of polygon ABCD if the coordinates of the vertices are A(5,-1), B(9,2), C(9,9), and D(0,5).
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the area of polygon ABCD if the coordinates of the vertices are A(5,-1), B(9,2), C(9,9), and D(0,5).
-------------------
A - B - C- D-A
+5 +9 +9 +0 +5
-1 +2 +9 +5 -1
-------------------
Add diagonals from upper left
5*2 + 9*9 + 9*5 = 10 + 81 + 45 = 136
Add diagonals from lower left
-1*9 + 2*9 + 9*0 + 5*5 = -9 + 18 + 25 = 34
-----------
Difference = 102
Area = 102/2 = 51 sq units
---------------------
PS It works for any # of points.