<p>I'm new here, and I'm writing the SAT this Saturday. I have a blue book question that I don't think has been answered here before.</p>
<p>It is page 721 #16. There is a picture of a square, with side length 3, with a shaded square lying inside diagonally. The question reads: In the figure above, what is the area of the shaded square?</p>
<p>Any help would be much appreciated.</p>
<p>Thanks.</p>
<p>Carly</p>
<p>edit: sorry I posted this as a response to a really old thread by accident first. Sorry!</p>
<p>Area of big square = 9
The four triangles around the shaded square are all congruent, with base=1 and height= 2. So area of one triangle is 1, and there are 4 triangles: 4(1) = 4.</p>
<p>I don’t get why the side lengths of the triangles have to be 1 and 2? How do you determine that? I mean I get that they have to add up to 3 of course, but I don’t see how you know the exact leg lengths.</p>
<p>His diagram has all you need: the angles of the triangles are all congruent – each triangle has one 90 degree angle, one that is x degrees and one that is 90-x. So the triangles are at least similar…but they all have the same length hypot (since the central figure is a square), so they are in fact more than just similar – they are congruent.</p>
<p>The original problem statement tells us that the lengths of the segments that I have marked in the figure are 1 and 2. Because all four triangles are congruent, identical in all aspects, internal angles, hypotenuse, and the two legs, they all have legs of lengths 1 and 2, respectively.</p>