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If the area of a regular hexagon is equal to the area of an equilatera
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05 Jan 2022, 10:17
05 Jan 2022, 10:17
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If the area of a regular hexagon is equal to the area of an equilateral triangle of side 12 cm, then the length, in cm, of each side of the hexagon is
A ) 4 √6
B ) 6 √6
C ) 2 √6
D ) √6
E ) 3√6
A ) 4 √6
B ) 6 √6
C ) 2 √6
D ) √6
E ) 3√6
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Joined: 06 Dec 2021
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Re: If the area of a regular hexagon is equal to the area of an equilatera
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18 Jan 2022, 00:18
18 Jan 2022, 00:18
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Area of Equilateral triangle with side a=12
A = (Sqrt3*a^2)/4 ...........(1)
Area of a regular Hexagon with side say h = (3Sqrt3*h^2)/2 ...........(2)
from eqn 1 n 2
h = 2 Sqrt6
Option C is correct
KarishmaB. Is it possible to solve it without using formula's.... by imagination and using geometry
A = (Sqrt3*a^2)/4 ...........(1)
Area of a regular Hexagon with side say h = (3Sqrt3*h^2)/2 ...........(2)
from eqn 1 n 2
h = 2 Sqrt6
Option C is correct
KarishmaB. Is it possible to solve it without using formula's.... by imagination and using geometry
If the area of a regular hexagon is equal to the area of an equilatera
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Updated on: 19 Sep 2023, 04:36
Updated on: 19 Sep 2023, 04:36
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Expert Reply
Arvind123 wrote:
If the area of a regular hexagon is equal to the area of an equilateral triangle of side 12 cm, then the length, in cm, of each side of the hexagon is
A ) 4 √6
B ) 6 √6
C ) 2 √6
D ) √6
E ) 3√6
A ) 4 √6
B ) 6 √6
C ) 2 √6
D ) √6
E ) 3√6
A regular hexagon is made up of 6 equilateral triangles. If area of the hexagon is equal to the area of another equilateral triangle, this tells me that area of each equilateral triangle within the hexagon is 1/6th the area of the large equilateral triangle. So we have two similar triangles with areas in ratio 1 : 6.
So length of sides will be in the ratio \(1 : \sqrt{6}\).
Since side of the large equilateral triangle (corresponding to sqrt(6)) is 12, the side of the hexagon's triangle will be \(\frac{12}{\sqrt{6}} = 2\sqrt{6}\)
Answer (C)
sivakumarm786 - "Imagination" isn't a method. It is an effective way of using concepts (including formulas) one understands thoroughly.
