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# geometry

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Three unit circles are tangent to each other, as shown in the figure .  Find the area of the shaded region

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Sep 21, 2020

#1
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If I'm not mistaken, the shaded area is 1.4488655 units squared.

Sep 21, 2020
#2
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Three unit circles are tangent to each other, as shown in the figure .  Find the area of the shaded region.

Hello Guest!

$$A=3\cdot(2r^2)+3\cdot(\frac{\pi r^2}{3})+ (2r\cdot r\sqrt{3})-3\cdot (\pi r^2)\\ A=r^2\cdot (6+\pi +2\sqrt{3}-3\pi)\\$$

$$A=2r^2\cdot (3+\sqrt{3}-\pi)\\ A=0.795229\ r^2$$

!

Sep 21, 2020
edited by asinus  Sep 21, 2020
edited by asinus  Sep 21, 2020