If the vertices of a polygon in counterclockwise order, are ( x1, y1 ) , ( x2, y2 ) , ... , ( xn, yn ) , show that the area of the polygon is A = 1 / 2 [ ( x1y2 - x2y1 ) + ( x2y3 - x3y2 ) + ... + ( xn - 1yn - xnyn - 1 ) + ( xny1 - x1yn ) ] . Use the formula above to find the area of a triangle with vertices (-3, 1), (0, 3), and (3, 2
If the vertices of a polygon in counterclockwise order, are ( x1, y1 ) , ( x2, y2 ) , ... , ( xn, yn ) , show that the area of the polygon is A = 1 / 2 [ ( x1y2 - x2y1 ) + ( x2y3 - x3y2 ) + ... + ( xn - 1yn - xnyn - 1 ) + ( xny1 - x1yn ) ] . Use the formula above to find the area of a triangle with vertices (-3, 1), (0, 3), and (3, 2
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 74E
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If the vertices of a
Use the formula above to find the area of a triangle with vertices (-3, 1), (0, 3), and (3, 2)
![If the vertices of a polygon, in counterclockwise order, are (x1, y1), (x2, Y2), . .. , (Xn, Yn),
show that the area of the polygon is
1
A
("142 – 22Y1) + (x2Y3 – X3Y2) + ·+ (Xn-1Yn – XnYn-1) + ("nY1 – X1Yn)] .
|](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F071ad70b-680b-44d6-b888-10a290f238d8%2Fc12a1bac-ae3d-43d6-bf74-6bbf92d6dd0e%2Flgzx7eq_processed.png&w=3840&q=75)
Transcribed Image Text:If the vertices of a polygon, in counterclockwise order, are (x1, y1), (x2, Y2), . .. , (Xn, Yn),
show that the area of the polygon is
1
A
("142 – 22Y1) + (x2Y3 – X3Y2) + ·+ (Xn-1Yn – XnYn-1) + ("nY1 – X1Yn)] .
|
![1
A = ; [(T142 – 12Y1) + (X2Y3 – X3Y2) + ·· · + (xn-1Yn – XnYn-1) + (XnY1 – 21Yn)] -
...
Remark: This is called the Shoelace Formula.
use calculus to find the area of the triangle with vertices (-3, 1), (0,3), and (3, 2)
Use the formula above to solve this problem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F071ad70b-680b-44d6-b888-10a290f238d8%2Fc12a1bac-ae3d-43d6-bf74-6bbf92d6dd0e%2Fp7m1mtk_processed.png&w=3840&q=75)
Transcribed Image Text:1
A = ; [(T142 – 12Y1) + (X2Y3 – X3Y2) + ·· · + (xn-1Yn – XnYn-1) + (XnY1 – 21Yn)] -
...
Remark: This is called the Shoelace Formula.
use calculus to find the area of the triangle with vertices (-3, 1), (0,3), and (3, 2)
Use the formula above to solve this problem.
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