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In the figure below, $ABCD$ is a parallelogram, $AD=18$ and $DC=27$. Segments $\overline{EG}$ and $\overline{FH}$ 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 12, 2022
 #1
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The area is given by  EG * DC   =  16 * 27   =  432

 

Note :   HF =  432  /18  =  24

 

cool cool cool

 Apr 12, 2022

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