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There are 5 circles with a radius of 3.34 cm each as shown in the picture. What is the trapezium with smallest area that contains these 5 given circles?

a trapezium with the two circles on the top with three on the bottom stacked adjacently

The image is a trapezium with the two circles on the top with three on the bottom stacked adjacently I tried adding the diameters of 3 to get the bottom, 2 to get the top then 2 to get the height but then the angle would cut through the bottom circle. I'm unsure how to figure out what length it has to be

James D
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  • Please note that the body of the post should be self contained. So move the necessary information from the title to the body of the post. Also you should tell us your thoughts and what you have already tried. – miracle173 Jun 04 '18 at 04:58
  • Well I have tried finding the area of the circles then the minimum lengths for each aspect (a b and h). But the angles at which the trapezium came in toward seemed unrealistic. Sorry for the formatting my first time on this platform – James D Jun 04 '18 at 05:03
  • please add this information to the post. How did you calculte the minmum length of a,b, and h. What property of the trapezoid should become minimal? I assume the area. Is this right? If so, how is the area of a trapezoid calculated? Please add this to your post. – miracle173 Jun 04 '18 at 05:18

1 Answers1

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Just by observation, it's when the sloping sides are tangent to both circles. In the picture, a sloping line which is tangent to both circles will remove more orange area above the tangent point on the bottom circle than the added area below it.

Phil H
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