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Polygon Overlap (Posted on 2017-04-17) Difficulty: 2 of 5

  
Side DE of square BCDE splits ΔABC into a smaller ΔAFG
and a quadrilateral BCGF. The area of ΔABC is twice that of
the square.

What is the value of Area(ΔAFG) / Area(BCGF) ?
  

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Solution solution Comment 1 of 1
The height of triangle ABC from A to base BC is four times the side length of the square and thus four times the height of trapezoid BCGF from its top GF to its base BC.

Let's assume the square is a unit square so the triangle has base 1 and height 4. FG has length 3/4. The trapezoid BCGF therefore has area (1 + 3/4)*1/2 = 7/8, while the full triangle ABC has area 2, leaving 9/8 for the smaller triangle AFG.

The ratio asked for is then 9/7.

  Posted by Charlie on 2017-04-17 10:49:34
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