June 24th, 2011, 09:06 PM  #1 
Newbie Joined: Jun 2011 Posts: 21 Thanks: 0  Finding Sides and area of trapezoid around two circles.
Find Sides and area of trapezoid around two circles with radius=1 and Radius=3. Here is the exact picture give by teacher (not drawn to scale) That was the only info given. Any guidance or suggestions on how to solve? 
June 24th, 2011, 10:57 PM  #2 
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0 
Assume the circles are externally tangent and the trapezoid is isosceles. The sides are and The area is I'm 99% certain that my answers are correct. 
June 25th, 2011, 07:58 AM  #3 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,981 Thanks: 1166 Math Focus: Elementary mathematics and beyond  Re: Finding Sides and area of trapezoid around two circles.
Orienting the trapezoid so the r = 3 circle is at the bottom and assuming the centers of the circles are in a line perpendicular to the base of the trapezoid, the angle in the bottom two corners is arctan(2) and the height of the trapezoid is 8.

June 25th, 2011, 09:46 AM  #4 
Newbie Joined: Jun 2011 Posts: 21 Thanks: 0  Re: Finding Sides and area of trapezoid around two circles.
Where did you get the number 2 from?

June 25th, 2011, 01:40 PM  #5 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,981 Thanks: 1166 Math Focus: Elementary mathematics and beyond  Re: Finding Sides and area of trapezoid around two circles.
From a mistake, sorry about that.

June 25th, 2011, 03:40 PM  #6 
Newbie Joined: Jun 2011 Posts: 21 Thanks: 0  Re: Finding Sides and area of trapezoid around two circles.
im still confused. how would i find the area of the trapezoid though? 
June 25th, 2011, 04:22 PM  #7 
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0 
Height 8 with bases and therefore area 
June 25th, 2011, 05:18 PM  #8 
Senior Member Joined: Feb 2010 Posts: 714 Thanks: 151  Re: Finding Sides and area of trapezoid around two circles.
Why can't the picture be drawn like this? Then the area is 30+16 sqrt(3)

June 25th, 2011, 07:42 PM  #9 
Newbie Joined: Jun 2011 Posts: 21 Thanks: 0  Re: Finding Sides and area of trapezoid around two circles.
How did you find the length of the sides?

June 25th, 2011, 08:12 PM  #10  
Senior Member Joined: Feb 2010 Posts: 714 Thanks: 151  Re: Finding Sides and area of trapezoid around two circles. Quote:
 

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