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In the figure below,  is a parallelogram,  and . Segments  and  are perpendicular to sides of the parallelogram as shown, and . 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]

 Dec 20, 2020
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The parallelogram has a base of 10 and a height of 18, so its area is 10*18 = 180.

 Dec 28, 2020

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