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In trapezoid $ABCD,$ $\overline{AB} \parallel \overline{CD}$. Find the area of the trapezoid.
 

 

 Jun 13, 2024
 #1
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Draw DE , CF  perpendicular to  AB

 

Let AE  = x

Let BF = 96 - (44 + x)  = 52 - x

Angle DAB = 70

tan DAB  = h /AE

tan(70)  = h/ x

h = x tan 70

 

tan (55)  = h / (52 - x)

h = (52 -x)tan (55)

 

So

 

x tan 70  = (52 -x) tan 55

 

Solving  for x   ≈ 17.785

 

h = x tan 70  =  17.785 tan 70

 

Area  =  (1/2)  17.785 * tan 70 *( 96 + 44) ≈ 3420 .5

 

 

cool cool cool

 Jun 14, 2024

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