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Find the area of this shape in the coordinate plane.

 

 Dec 14, 2020
 #1
avatar+156 
+1

You can split this into smaller parts and calculate the area, or use the Shoelace Theorem. Since I can't demonstrate splitting the shape here, I can use the shoelace theorem. 

 

Either way will give you 87/2 .

 Dec 14, 2020
 #2
avatar+114221 
+1

Thx, Firebolt....here's another way with something known as Pick's Theorem

 

Lattice points =  points with integer coordinates

 

Area = [  lattice points in the interior of the  figure ]  + [ lattice points on the  boundary  / 2 ]    - 1

 

So we have

 

50  +  16/2   -  1   =

 

50  + 8  -  1   =

 

57

 

 

cool cool cool

 Dec 14, 2020

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