Question 240236
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If the circles just touch each other, then you can draw a line connecting the centers of each pair of adjacent circles creating an equilateral triangle of side length 7 (2 times 3.5).  The area of an equilateral triangle is given by:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ A\ =\ \frac{s^2\sqrt{3}}{4}]


There are four areas inside of this equilateral triangle, three *[tex \LARGE \frac{\pi}{3}] circle sectors and the area we seek.


The area of a circle sector is given by:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ A\ =\ \frac{1}{2}r^2\Theta]


where *[tex \LARGE \Theta] is the central angle of the sector.


So, the area we want is the area of the equilateral triangle minus three times the sector area.



*[tex \LARGE \ \ \ \ \ \ \ \ \ \ A\ =\ \frac{7^2\sqrt{3}}{4}\ -\ 3\left(\frac{1}{2}(3.5)^2\left(\frac{\pi}{3}\right)\right)]


You just need to simplify but I would leave the answer in terms of the radical and *[tex \LARGE \pi]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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