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Regular hexagon ABCDEF is symmetrical about the x-axis and the y-axis in a rectangular coordinate plane, as shown above. If the coordinates of point D are (2,0), what is the area, in square units, of rectangle BCEF?
- a)√3
- b)3
- c)2√3
- d)4√3
- e)8√3
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Regular hexagon ABCDEF is symmetrical about the x-axis and the y-axis ...
Given:
- Regular hexagon ABCDEF
- This means, each interior angle of this hexagon will measure 120o
- (Here’s how you can calculate this: Measure of each angle of a regular n-sided polygon =
- So, for a regular hexagon (n =6), each interior angle =
- Let each side of this hexagon measure a units
- Hexagon ABCDEF is symmetrical about the x-axis and the y-axis.
- This means, the center of the coordinate plane O(0,0) lies at the exact center of the hexagon
- Point D(2,0)
- To find: ar(Rectangle BCEFApproach:
- We need to find the value of Ar(Rectangle BCEF)
- Note that since the origin lies at the exact center of the hexagon, and hence also at the center of rectangle BCEF, it will divide rectangle BCEF into 4 smaller and identical rectangles.
- Let’s label one of these rectangles as OGCH
- So, Ar(Rectangle BCEF) = 4*ar(Rectangle OGCH)
- (Here’s how you can calculate this: Measure of each angle of a regular n-sided polygon =
- This means, each interior angle of this hexagon will measure 120o
2. ar(Rectangle OGCH)= CG*CH
- Since the hexagon is symmetrical about the x-axis,
- And, since the hexagon is symmetrical about the y-axis,
- So, if we can find CG and a, we can answer the question.
. Now, OG + GD = OD
- We know the value of OD.
- Using trigonometric ratios in right triangle CGD, we can express DG in terms of hypotenuse a (Note that the hypotenuse of this triangle is the side of regular hexagon ABCDEF, and so, is equal to a units)
- We already know the value of OG in terms of a
- So, from this equation, we can find the value of a
4. Also, in right triangle CGD, using trigonometric ratios, we can express CG in terms of hypotenuse a.
- So, once we know the value of a, we can find the value of CG as well
Working Out:
- Finding the value of a
- Finding the value of CG
Working towards the final answer
- Therefore, ar(Rectangle BCEF)
- Looking at the answer choices, we see that the correct answer is Option D
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Regular hexagon ABCDEF is symmetrical about the x-axis and the y-axis in a rectangular coordinate plane, as shown above. If the coordinates of point D are (2,0), what is the area, in square units, of rectangle BCEF?a)√3b)3c)2√3d)4√3e)8√3Correct answer is option 'D'. Can you explain this answer?
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Regular hexagon ABCDEF is symmetrical about the x-axis and the y-axis in a rectangular coordinate plane, as shown above. If the coordinates of point D are (2,0), what is the area, in square units, of rectangle BCEF?a)√3b)3c)2√3d)4√3e)8√3Correct answer is option 'D'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Regular hexagon ABCDEF is symmetrical about the x-axis and the y-axis in a rectangular coordinate plane, as shown above. If the coordinates of point D are (2,0), what is the area, in square units, of rectangle BCEF?a)√3b)3c)2√3d)4√3e)8√3Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Regular hexagon ABCDEF is symmetrical about the x-axis and the y-axis in a rectangular coordinate plane, as shown above. If the coordinates of point D are (2,0), what is the area, in square units, of rectangle BCEF?a)√3b)3c)2√3d)4√3e)8√3Correct answer is option 'D'. Can you explain this answer?.
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