SOLUTION: The trapezoid shown is divided into four triangles by its diagonals. The area of two triangles are indicated(9 and 25). What is the area of the whole trapezoid? <pre> Note: Ima

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Found 2 solutions by  lotusjayden, ikleyn:
Answer by lotusjayden(18)   (Show Source): 

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Answer by ikleyn(52835)   (Show Source): 

You can put this solution on YOUR website!
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Let "a" be the shorter base of the trapezoid;

let "b" be the longer base of the trapezoid.


The triangles of the areas 9 and 25 square units are similar, 
with the similarity coefficient of  (smaller to larger).


Let h be the height of the smaller triangle drawn to its base "a";

Let H be the height of the larger triangle drawn to its base "b".


Then from the similarity of triangles,  b = ;  H = .


We have then   =  =  = ;

              h + H =  = .


The area of the trapezoid is  

    Area =  =  = ;

    but   = the area of the upper triangle = 9;  hence  ah = 2*9;  therefore

    Area =  = 32*2 = 64 square units.


ANSWER.  The area of the trapezoid is 64 square units.


Solved.