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What is the area of this figure? Enter your answer in the box. unitsĀ² An irregular heptagon is graphed on a coordinate plane. The horizontal x-axis ranges from negative 6 to 6 in increments of 1. The vertical y-axis ranges from negative 6 to 6 in increments of 1. The vertices of the heptagon are located at begin ordered pair negative 5 comma 3 end ordered pair, begin ordered pair negative 4 comma 5 end ordered pair, begin ordered pair negative 2 comma 3 end ordered pair, begin ordered pair 3 comma 4 end ordered pair, begin ordered pair 4 comma 3 end ordered pair, begin ordered pair 4 comma negative 3 end ordered pair, and begin ordered pair negative 3 comma negative 3 end ordered pair.

Guest Mar 3, 2017
 #1
avatar+87309 
+5

We can use something called "Pick's Theorem to solve this.....

 

The theorem says that as long as the vertices of a figure lie on integer coordinates .....like yours....we can calculate the area as :

 

 B/2 + I   - 1           

 

Where B is the number of boundary points  [" boundary points" are defined as the number of time the edges of the figure intersect integer coordinates...i,e.....the intersection of the grid lines ] 

 

And I   is the number of interior points  [ again....these are the number of interior points that lie on  integer coordinates]

 

We have 14 boundary points   and 27 interior points

 

So.....the area  =   14/2 + 27 - 1   =  7 + 27 - 1  =  34 - 1   =  33 sq units

 

Heres's a pic : 

 

 

 

cool cool cool

CPhill  Mar 3, 2017

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