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Find the area of the shaded poygons.

 

 Mar 19, 2021
 #1
avatar+91 
+2

We can use Pick's rule for the area:

 

\(A=I+{\frac {p} {2}}-1\)

-Where I is the points inside the figure and p is the points on the perimeter.

 

There are 5 points inside and 10 on the perimeter.

 

A = 5 + 10/2 - 1

A = 5+5-1

A=9

 

Therefore the area is 9 square units.

 Mar 19, 2021
 #2
avatar+956 
+2

If you don't know Pick's Theorem, you could also do it this way:

 

 

shaded = (area of total region) - (area not shaded)

\((4 \cdot 4) - (\frac{2 \cdot 3}{2} + \frac{1 \cdot 1}{2} + 1 + \frac{1 \cdot 2}{2} + \frac{1 \cdot 3}{2})\)

\(16 - 7\)

\(\boxed{9}\)

 

You could also find the area of the shaded region directly, which is just made out of squares and triangles.

 

\(\frac{2 \cdot 2}{2} + 2 + \frac{3 \cdot 1}{2} + 1 + \frac{2 \cdot 1}{2} + \frac{3 \cdot 1}{2}\)

\(2 + 2 + \frac{3}{2} + 1 + 1 + \frac{3}{2}\)

\(\boxed{9}\)

 Mar 20, 2021

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