<p>By no means all SAT “drawn to scale” geometry questions can be cracked through visual estimating, especially those on areas (or volumes :)).</p>
<p>Actually, #20 is a lucky exception: if you imagine cutting that square along the lines RT and US, and then along all four arcs, you’ll get four pairs of respectfully congruent pieces (white=gray), which tells us that the shaded area is equal to the unshaded and is consequently equal to half area of the square, 6x6/2=18.</p>
<p>Incidentally. two other geometry questions from the same test can be solved by visual estimating.</p>
<h1>9:</h1>
<p>marking on the edge of a piece of paper (think answer sheet) the length of QS and moving that piece around you immediately see that QS=SP=SN=NR=6, so
PS+SN+NR+RP = 30.
The figure, interestingly enough, is constructed as a visual illusion: QS appears longer then SP.</p>
<h1>30:</h1>
<p>if you have only 3 sec. left on this question, w=3 seems like an accurate guesstimate.
Guess what? It’s the right answer!</p>
<p>Edit.
Visual estimating applies to “drawn to scale” graphs as well.</p>
<h1>33: you can see the answer right away: 1.5. Does the ETS make our life more difficult by placing tic marks on the axis? Quite au contraire.</h1>
<p>I am not advocating forgoing mathematically tight solutions in favor of crude measuring/guesstimating. As a matter of fact, I enjoy “proving” my answers. But in a time crunch anything goes, as long your drawn chances of getting the right answer are good on The Scale of Things. :D</p>