Question 1209518
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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>
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>
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>
ANSWER: 1/6<br>
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Comment to Edwin's comment....<br>
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>
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... added later to pacify tutor @ikleyn, who doubts that problems like this can be solved by choosing a "nice" case....<br>
Each diagonal of a rhombus divides the rhombus into two congruent triangles.<br>
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>
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>