Plot the points, draw the polygon, and calculate its area using the Shoelace Theorem. (a) (1, 3), (2, 1), (5, 0), (6,4), (4, 2) (b) (0, 0), (4, -1), (7, 2), (6,5), (3, 7), (1,4)

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter8: Areas Of Polygons And Circles
Section8.5: More Area Relationships In The Circle
Problem 9E
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Exercise set 2 part a and b please!

Shoelace Theorem:
Suppose the polygon P has vertices (a₁, b₁), (a₂, b₂),... (an, bn) listed in clockwise order.
Define an+1 = a₁, bn+1 = b₁. Then, the area of P can be calculated using the formula:
area of P =
NII
n
k=1
det [1
[ακ
ak+1]
bk+1]
Note that this is the absolute value of the sum of determinants.
Exercise Set 2:
Plot the points, draw the polygon, and calculate its area using the Shoelace Theorem.
(a) (1, 3), (2, 1), (5, 0), (6, 4), (4, 2)
(b) (0, 0), (4, -1), (7,2), (6,5), (3, 7), (1, 4)
Transcribed Image Text:Shoelace Theorem: Suppose the polygon P has vertices (a₁, b₁), (a₂, b₂),... (an, bn) listed in clockwise order. Define an+1 = a₁, bn+1 = b₁. Then, the area of P can be calculated using the formula: area of P = NII n k=1 det [1 [ακ ak+1] bk+1] Note that this is the absolute value of the sum of determinants. Exercise Set 2: Plot the points, draw the polygon, and calculate its area using the Shoelace Theorem. (a) (1, 3), (2, 1), (5, 0), (6, 4), (4, 2) (b) (0, 0), (4, -1), (7,2), (6,5), (3, 7), (1, 4)
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