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A isosceles trapezoid has a base of length 12 and a top of length  4 .  Find its height (length of the red line) if   $ AC  \perp  BD $.

 

 Jan 23, 2021
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Call the intersection  of   AC  and  BD  =   M

 

Because   AC is  perpendicular to  BD,  then in triangle  BMC, angle  BMC is right

 

And   CM = BM   = 12/sqrt (2)=  legs  of  BMC

 

So the area of this triangle  is    product of the  legs / 2  =   (1/2)  (12/sqrt 2) ^2  =  144/ 4  =  36

 

But the area  of this triangle also  =  (1/2) 12  * altitude

 

36  = (1/2) 12  (altitude

36  = 6 * altitude

6  = altitude

 

And triangle  DMA  is similar to  to triangle BMC

So the height  of  triangle  DMA  =  4/12  *  6  =   2

 

So.....  the height of the trapezoid =    6 + 2   =   8

 

 

cool cool cool

 Jan 23, 2021

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