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In the figure shown here, the distance between any two horizontally or vertically adjacent dots is one unit. What is the area of the shaded polygon in square units?

 Apr 19, 2019
 #1
avatar+103122 
+1

The easiest thing here is to use something known as "Pick's Theorem"....this only works when the vertexes of the figure are lattice points

 

Lattice point  =  a point with integer coordinates

 

Area  =   

 

Number of lattice points on the  boundary of the figure / 2  + number of interior lattice points  - 1

 

So we have  

 

Boundary lattice points  = 9

Interior lattice points  = 17

 

Area  =   9/2 + 17 - 1   =   4.5 + 16  =   20.5 units^2

 

 

 

cool cool cool

 Apr 19, 2019
 #2
avatar+200 
+1

Thanks CPhill!

sudsw12  Apr 19, 2019

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