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A circle is inscribed in the right trapezoid with base length 22 and 35.  Find the area and perimeter of the trapezoid.

 

 Jan 18, 2021
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See the following image :

 

 

 

 

Draw perpendicular CE  from  the top right vertex of the trpezoid to the base

 

We have  right  triangle  CED with  CE = 2r  , ED =  (35-22) = 13     and  the  hypotenuse CD  =  (22 - r) + ( 35 - r)  = (57 - 2r)

 

So

 

ED^2 +CE^2  = CD^2

 

13^2 +  (2r)^2   =  ( 57  -2r)^2

 

Solving this for positive r  gives us    r  = 770/57

 

The   area of the  trapezoid = (1/2) (2r) (sum of bases)  =  (1/2) (2 * 770/57) ( 57)  =  770

 

The perimeter =   2(770/57) + (35 + 22)  + 57 - 2(77/57)   =  114

 

cool cool cool

 Jan 18, 2021
edited by CPhill  Jan 18, 2021

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