<p>In the figure above, sides AB and CD of a trapezoid ABCD are congruent. Trapezoids congruent to ABCD are placed adjacent to one another, sharing one of their nonparallel sides as shown. This is continued until the trapezoids form a closed ring. How many trapezoids, including the 3 shown, are needed to form the closed ring?</p>
<p>Answer is 18. I found an explanation on CC but it was to vague; can you please explain it in simple terms? I am unfamiliar with trapezoids.</p>
<p>first let us name the center of circle O for easier explanation. Then you will notice that OAD is a triangle and will easily calculate angle AOD which equals 180-80-80 = 20. Then you will notice that 20x18 = 360, which is the required degree to form a whole circle => the answer, therefore, is 18 trapezoids</p>
<p>If you consider the regular n-gon formed by the outer perimeter of the “ring,” the interior angle will have measure 160 deg, so the exterior angles each measure 20 deg. The sum of the exterior angles in a convex polygon is 360 deg, so the number of sides/trapezoids is 360/20 = 18.</p>
<p>I think that both explanations above (all very good and clear) have been posted on CC in the past. In general, it pays to look for more than an answer via Google Search THIS site. </p>
<p>Fwiw, this type of problems is very SAT typical. Extremely hard for anyone who has not made much of an effort to learn basic geometry (or not have had much of a teacher as it happens in 90 percent of the cases) and extremely easy and trivial for anyone who knows basic geometry and recognizes simple constructions and visualizations. </p>
<p>@Sparkkid1234 Thank you so much! That was the easiest explanation ever! :)</p>
<p>@MITer94 thanks :)</p>
<p>@xiggi These explanations are NEVER been posted on CC. Only one post I found in which the explanation was very conplex. You can try to Google this question. This is not from the blue book.
The problem is that I never paid attention to my maths class till middle school. I started studying hard after 10th grade. As a result there are lots of gaps in my knowledge. After studying extensively, 90% of the gap seems to be filled. </p>
<p>But my problem lies with VISUALIZATION; almost any question that needs creative viaualization in geometry intimidates me.</p>
