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Find the area of each shaded figure.

 

 Apr 24, 2020
 #1
avatar+21017 
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I'm guessing that yo're supposed to use Pick's Theorem:

  Area  =  (Number of Interior Points) + ½·(Number of Boundary Points) - 1

 

For instance, in the figure at top-right, there are 3 interior points and 12 boundary points, so:

   Area  =  (3) + ½·(12) - 1  =  3 + 6 - 1  =  8

 

A point is one of the coordinate points on the graph paper. 

An interior point is one of these points found inside the figure.

A boundary point is any point that is on the edge of the figure.

 

For the bottom-right figure, there are 8 interior points and 4 boundary points:

   Area  =  8 + ½·4 - 1  =  9

 Apr 24, 2020
 #2
avatar+30 
+1

Assuming that each square is one unit, the first one is \(2*1+5*2+1*1=13\) units

 

2. This is two equal triangles. So \((4*2)/2+(4*2)/2\)=4

 

3.  There are two pentagons of equal area. So the area would be \(7.5*2=15\)

 

4. Make a 4x5 square around it. Subtract 4 from one of the outside triangles. Subract 2 from another. Finally subtract 5 from the last. So \(20-4-5-2=9\).

 Apr 28, 2020

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