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In the figure below, ABCD is a parallelogram, AD = 18 and DC = 27. Segments EG and FH are perpendicular to sides of the parallelogram as shown, and EG = 16.What is the area of the parallelogram?

 

[asy] size(7cm);pair b=(-sqrt(68),16); pair g=(0,0); pair s=(27,0); pair y=b+s;pair a=(8,16); pair u=(8,0);pair o=g+0.15*(b-g);pair e=o+(64/3,4/3*sqrt(68));dot(b); dot(o); dot(g); dot(u); dot(s); dot(a); dot(y); dot(e);draw(y--e);draw(g--o);draw(o--e,dashed);draw(a--u,dashed);draw(o--b,MidArrow(TeXHead));draw(s--e,MidArrow(TeXHead));draw(b--b+0.94*(y-b),MidArrow(TeXHead));draw(y+0.98*(b-y)--y,MidArrow(TeXHead));draw(g--g+0.96*(s-g),MidArrow(TeXHead));draw(s+0.96*(g-s)--s,MidArrow(TeXHead));draw(rightanglemark(a,u,g,50));draw(rightanglemark(o,e,s,50));label(

 Apr 8, 2019
 #1
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0

Area of parallelogram  = height * width

 

height = EG   = 16

 

width  = AB =  DC  = 27

 

So

 

16 * 27  =

 

432 units^2

 

 

cool  cool cool

 Apr 8, 2019

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