1) 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. The distance from the center of the barn to the midpoint of one of the sides is 50√3 feet What is the area of the enclosed space?
i dont have its OA
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plz explain
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sana.noor
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Last edited by sana.noor on Thu Sep 26, 2013 4:59 am, edited 1 time in total.
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theCodeToGMAT
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Assuming you meant the distance as √503.
According to me,
Area enclosed = 6 * area of equilateral triangle with altitude √503
√3/2 * side = √503 --> side = 2 * √(503/3)
Area = 6 * √3/4 * 4 * 503/3 = 1006√3
According to me,
Area enclosed = 6 * area of equilateral triangle with altitude √503
√3/2 * side = √503 --> side = 2 * √(503/3)
Area = 6 * √3/4 * 4 * 503/3 = 1006√3
Last edited by theCodeToGMAT on Thu Sep 26, 2013 5:12 am, edited 1 time in total.
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Resp007
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hi,
Since every side and angles are same so we have a 6 equilateral triangles, with heights given for each. To find the total are we need base or one side of the triangle: (see fig)
So answer = 15*(root 3)*1000 sq units, assuming, ht = 503√ feet = 50* (root 3).
Does it make sense? :/
Since every side and angles are same so we have a 6 equilateral triangles, with heights given for each. To find the total are we need base or one side of the triangle: (see fig)
So answer = 15*(root 3)*1000 sq units, assuming, ht = 503√ feet = 50* (root 3).
Does it make sense? :/
sana.noor wrote:1) 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. The distance from the center of the barn to the midpoint of one of the sides is 503√ feet What is the area of the enclosed space?
i dont have its OA
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Brent@GMATPrepNow
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I'm assuming that the barn is in the center of this hexagon.sana.noor wrote:1) 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. The distance from the center of the barn to the midpoint of one of the sides is 50√3 feet. What is the area of the enclosed space?
Since all sides are the same length, and all angles have the same measure, we have a "regular" hexagon.
If we draw lines from the center to the 6 vertices, we get 6 equilateral triangles.
The distance from the center of the barn to the midpoint of one of the sides is 50√3 feet. So, we get:
Notice that we can now create a 30-60-90 right triangle.
If we compare the red triangle to the "base" 30-60-90 triangle . . .
. . . we can see that the red triangle is 50 times bigger than the "base" triangle [since 50√3 is 50 times greater than √3]
So, the other two sides of the red triangle must have lengths 50 and 100
From here, we can see that each side of this equilateral triangle has length 100.
IMPORTANT: For test day, be sure to memorize the formula for the area of an equilateral triangle. Area = √3(side)²/4 [yes, we can also use other triangle area formula here, but I wanted to point out another useful formula to know]
So, the area of this equilateral triangle = √3(100)²/4
= 2500√3
Of course, that's the area of just one of the 6 equilateral triangles.
So, the ENTIRE area of the hexagon = 6( 2500√3) = [spoiler]15,000√3[/spoiler]
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
