GMAT question - The square ABCD has sides of length 4. Point E is ha... - Review
Type: Problem Solving
Difficulty: 
The square ABCD has sides of length 4. Point E is half way between A and D, point F is half way between B and C and point G is half way between E and F. What is the area enclosed by the polygon ABCDEG?
%20-%20(%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%202%20%5Ctimes%202)%20%5C%5C%0D%0A&=%2016%20-2%20%5C%5C%0D%0A&=%2014%0D%0A%5Cend%7Bsplit%7D%0D%0A)
- 16
- 14
- 12
- 10
- 8
Explanation
The key to this question will be keeping track of all the information we are provided with.
Draw diagrams
We can do this by drawing diagrams on your note board.
From the question we have,
"The square ABCD has sides of length 4."
And then,
"Point E is half way between A and D, point F is half way between B and C and point G is half way between E and F."
And finally,
What is the area enclosed by the polygon ABCDEG?
Work out the area
You can see that the area of the shaded region ABCDEG is equal to the area of square ABCD minus the area of triangle AEG.
The area of the polygon ABCDEG is 14 and the correct answer is B.
This is a terrible explanation.
Just do 16 minus the area of the missing triangle.
16 - [1/2 b*h] of the missing triangle
16 - [1/2 (2*2)]
= 14
I agree, it is clearer if you treat this as the area of the square minus the triangle that has been removed. I have updated the explanation to reflect this.
But for those who have a little knowledge, it will be very useful
This is a stupid question. No where does it say that point E has to be on the line AD. Point E could be internal to the square and still be halfway from both A and D.