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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("$A$",b,NW); label("$D$",g,SW); label("$C$",s,SE); label("$B$",y,NE); label("$H$",o,WSW); label("$F$",e,ENE); label("$E$",a,N); label("$G$",u,S); [/asy]

 Nov 24, 2020
 #1
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Link::::https://web2.0calc.com/questions/in-the-figure-below-abcd-nbsp-is-a-parallelogram-ad-18-nbsp-and-dc-27-nbsp-segments-eg-nbsp-and-fh-nbsp-are-perpendicular-to-sides-of

 Nov 24, 2020
 #2
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The area of a parallelogram can be found by multiplying side times the height to that side.

Since you will get the same answer using whatever side you want to use:

Area  =  FH x AD  =  EG x DC

--->        FH x 18  =  16 x 27

--->                FH  =  24

(Solved by Geno)

 Nov 24, 2020

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