document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209518>Question 1209518</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (36) PQRS is a rhombus, W is the midpoint of PQ, T is the midpoint of PS and V is the intersection point of QT and SW. What fraction of rhombus PQRS is quadrilateral PWVT?\r<BR>\n" );
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document.write( "Link to diagram: https://ibb.co/PsrxgPwG </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849560 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849560\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "From the statement of the problem, the result is independent of the shape of the rhombus.  So choose the \"nice\" case where it is composed of two equilateral triangles.<br><BR>\n" );
document.write( "In each triangle, the three medians divide the triangle into 6 congruent 30-60-90 right triangles, so quadrilateral PWVT has area 2/6 = 1/3 of the area of that equilateral triangle.<br><BR>\n" );
document.write( "And since the two equilateral triangles are the same size, the area of quadrilateral PWVT is 1/6 of the area of the rhombus.<br><BR>\n" );
document.write( "ANSWER: 1/6<br><BR>\n" );
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document.write( "Comment to Edwin's comment....<br><BR>\n" );
document.write( "If a geometry problem is stated generally so that the desired result is true in all cases, then it is a very powerful problem-solving strategy to solve the problem by selecting a specific case for which the desired result is easily obtained....<br><BR>\n" );
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document.write( "... added later to pacify tutor @ikleyn, who doubts that problems like this can be solved by choosing a \"nice\" case....<br><BR>\n" );
document.write( "Each diagonal of a rhombus divides the rhombus into two congruent triangles.<br><BR>\n" );
document.write( "In each of those triangles, the three medians divide the triangle into six triangles whose areas are equal; that means the area of quadrilateral PWVT (composed of 2 of the 6 smaller triangles in its triangle) is 2/6 = 1/3 the area of its triangle and thus 1/6 the area of the whole rhombus.<br><BR>\n" );
document.write( "In my original response above, I simply chose to use a rhombus composed of two equilateral triangles to make it easier to see the solution.<br><BR>\n" );
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