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The honeycomb figure above consists of six identical regular
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17 Jan 2020, 11:31
17 Jan 2020, 11:31
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60% (01:32) correct
39% (01:47) wrong based on 38 sessions
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#greprepclub The honeycomb figure above consists of six identical regular hexagons,.jpg [ 79.24 KiB | Viewed 1913 times ]
The honeycomb figure above consists of six identical regular hexagons, each with side length \(2 \sqrt{3}\) .
Quantity A |
Quantity B |
The total area of the honeycomb |
\(180\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Re: The honeycomb figure above consists of six identical regular
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19 Jan 2020, 03:55
19 Jan 2020, 03:55
1
We must recognize that there are 6 equilateral triangles in a regular hexagon.
Area of equilateral triangle = √3/4 * Side^2
Given Side = 2√3. Area of one triangle = √3/4 (2√3)^2 => 3√3
Area of 6 triangles = 6 * 3√3 => 18√3, This is also the area of one hexagon.
Total area of the honeycomb = 6 X Area of 1 hexagon = 6 * 18√3 = 108√3.
Value of √3 is approximately 1.7.
Therefore, 108 * 1.7 is approximately 183.6, which is greater than option B. So choice A is correct.
Area of equilateral triangle = √3/4 * Side^2
Given Side = 2√3. Area of one triangle = √3/4 (2√3)^2 => 3√3
Area of 6 triangles = 6 * 3√3 => 18√3, This is also the area of one hexagon.
Total area of the honeycomb = 6 X Area of 1 hexagon = 6 * 18√3 = 108√3.
Value of √3 is approximately 1.7.
Therefore, 108 * 1.7 is approximately 183.6, which is greater than option B. So choice A is correct.
gmatclubot
Re: The honeycomb figure above consists of six identical regular [#permalink]
19 Jan 2020, 03:55
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