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14 Nov 2018, 09:37
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
74% (01:18) correct
26%
(01:47)
wrong
based on 870
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Land for a pasture is enclosed in the shape of a 6-sided figure; all sides are the same length and all angles have the same measure. What is the area of the enclosed land?
(1) Each side is 8 meters long.
(2) The distance from the center of the land to the midpoint of one of the sides is 4\(\sqrt{3}\) meters.
(1) Each side is 8 meters long.
(2) The distance from the center of the land to the midpoint of one of the sides is 4\(\sqrt{3}\) meters.
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14 Nov 2018, 09:46
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Given: 6 sided figure with equal sides and angles. So it is a regular hexagon, which can be divided into 6 equilateral triangles which share one vertex at the center of the hexagon.
Stmt 1: Given that each side is 8, we can find the area of each equilateral triangle to be sqrt(3)*8*8/4 and then multiply the result by 6 to get the area of the hexagon. Hence sufficient.
Stmt 2: The statement essentially gives us the length of the perpendicular bisector of an equilateral triangle = sqrt(3)*side/2 = 4*sqrt(3), hence side can be found, next the area of each equilateral triangle can be calculated, which multiplied by 6 will give us the area of the hexagon. Hence sufficient.
Therefore, Option D is the best choice!
Stmt 1: Given that each side is 8, we can find the area of each equilateral triangle to be sqrt(3)*8*8/4 and then multiply the result by 6 to get the area of the hexagon. Hence sufficient.
Stmt 2: The statement essentially gives us the length of the perpendicular bisector of an equilateral triangle = sqrt(3)*side/2 = 4*sqrt(3), hence side can be found, next the area of each equilateral triangle can be calculated, which multiplied by 6 will give us the area of the hexagon. Hence sufficient.
Therefore, Option D is the best choice!
14 Nov 2018, 10:09
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gmatbusters
An additional solution to the one above, relying on the logic of regular polygons:
Since all sides and (internal) angles are equal, the polygon is regular.
The only thing you can do to a regular polygon is make it larger or smaller; all other ratios are fixed.
So, given any one of the polygons parameters (length of side, area, cross-section, whatever you like), you know EXACTLY how to draw the polygon.
This implies that you can calculate all of its parameters.
Since both (1) and (2) provide us with one of the parameters, they fix ALL the parameters of the polygon.
Then (D) is correct.
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