Doubt from practice quiz bank I Geometry

GRE Quant Problem Solving
1

I was trying to solve this question by determining the length of DE and EC. I want to sense-check my deductions which are allowing me to do this.

  • I first concluded that DF and EC will be parallel to each other, as they are both perpendicular to line DE.
  • This means that I can construct a rectangle, drawing a line from point F to EC (meeting it at say point S)
  • Angle AFD which is equal to 45 degree = angle FCD
  • This will help me find the area of the constructed rectangle separately and the small triangle- adding these to make the polygon.
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Does this make sense?

I recognise that Greg’s way of solving this by extendeding AB is much quicker and straightforward, but I still wanted to sense-check these conclusions for my knowledge. Thanks!

2

No?

3

Sorry my bad, typo, I meant AFD=ACE because FD II CE

4

Sure, that step is indeed correct

5

Awesome, thanks!