ABCDEF is a regular hexagon. P, Q and R are mid-points of AB, CD and EF respectively. Ratio of areas of triangle PQR to hexagon is
a) 1 : 2 b) 1 : 3 c) 2 : 3 d) 4 : 9 e) 3 : 8
Answer e
Source of this question is from a handout received in class.
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Geometry- Hexagon
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s91arvindh
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Hi s91arvindh,
Hexagon's are exceptionally rare on Test Day, so this question is not likely to show on the actual exam.
Before offering a solution, I'm going to give you some hints and let you "play" with this question a bit:
1) A regular hexagon is a 6-sided shape with 720 degrees.
2) Each of the angles in a regular hexagon is 120 degrees.
3) Put a dot in the middle of the hexagon and draw lines to each of the vertices and you'll have 6 identical equilateral triangles.
4) This question is perfect for TESTing VALUES. Try picking a value for a side length and see what you can figure out from there.
GMAT assassins aren't born, they're made,
Rich
Hexagon's are exceptionally rare on Test Day, so this question is not likely to show on the actual exam.
Before offering a solution, I'm going to give you some hints and let you "play" with this question a bit:
1) A regular hexagon is a 6-sided shape with 720 degrees.
2) Each of the angles in a regular hexagon is 120 degrees.
3) Put a dot in the middle of the hexagon and draw lines to each of the vertices and you'll have 6 identical equilateral triangles.
4) This question is perfect for TESTing VALUES. Try picking a value for a side length and see what you can figure out from there.
GMAT assassins aren't born, they're made,
Rich
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s91arvindh
- Junior | Next Rank: 30 Posts
- Posts: 22
- Joined: Sat Apr 19, 2014 5:24 am
Hi Rich,
Thanks a lot for giving a direction to solve this question,
I tried your method with the values of angles,
The area of triangle in the hexagon will be 5*1/2*b*h
I have considered Side as 4, The height of the triangle will be 2squareroot(3)
Area of triangles in hexagon will be 5*1/2*4*2squareroot(3)
Stuck after this..
But when I drawn midpoints as per the question.
There was another hexagon inscribed ( Drawn in brown color)
So can we use the inscribed hexagon as hint for solving this question.
Thanks
s91arvindh
