5 unit circles are placed with their centers on a square grid. What is the total green area?

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Note:
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The centers of the circles are
$(-1, 1), (1,1), (0,0), (-1,-1), (1,-1)$
.

$3 + 3\pi$
$3 + 4 \pi$
$4 + 3 \pi$
$4 + 4 \pi$

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Relevant wiki: Length and Area - Composite Figures$\quad$

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The figure is symmetrical about its midpoint,

so we can split it into 4 equal regions as shown above.

If we want to find the area of the entire region,

it is equivalent to 4 times the area of the figure below.

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The area of the figure on the consists of a dark green circle and a light green region.

The area of the dark green circle is just the area of a unit circle, $\pi r^2 = \pi$ .

The area of the light green region is the area of a square with side length 1, minus the area of a quarter of a unit circle:

$1^2 - \dfrac14 \pi \cdot 1^2 = 1- \dfrac14\pi.$

Thus, the total area of the figure on the right is $\pi + \left( \dfrac14 - \dfrac14\pi\right) = 1 + \dfrac34\pi$ .

Multiply this number by 4 gives us the desired answer $\boxed{4+3\pi }$ .