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# geometry

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Find the area of the shaded poygons.

Mar 19, 2021

#1
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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
+944
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If you don't know Pick's Theorem, you could also do it this way:

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

$$16 - 7$$

$$\boxed{9}$$

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