swerve wrote:A barn 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 space?
1) Each side is 100 feet long.
2) The distance from the center of the barn to the midpoint of one of the sides is 50\sqrt{3} feet.
The OA is D
Source: Veritas Prep
Given that the 6-sided figure has sides of the same length and have the same angle, the figure is a regular hexagon. Note that each interior angle of a hexagon is 120º and the simply by knowing the side or diagonal of the hexagon, we can compute its area. Thus, each statement by itself is sufficient.
You may visualize that a regular hexagon can be divided into 6 equal equilateral triangles. And the area of an equilateral triangle can be known by only knowing its side.
So, the area of a regular hexagon = 6*(Area of an equilateral triangle)
Area of a regular hexagon = 6*(√3s^2/4) = (3√3/2)*s^2, here s = side of the regular hexagon
Pl. refer to the following image.
Refer to the following image to get why Statement 2 is also sufficient.
Here, we have (√3/2)s = 50√3 => we get unique value of s = 100. Sufficient.
The correct answer:
D
Hope this helps!
-Jay
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