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04 Jan 2021, 09:44
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D
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Difficulty:
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71% (01:39) correct
29%
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Seven identical circles - each of radius 1 inch - are arranged tangentially to one another as shown above. What is the area enclosed by the hexagon connecting the centers of the outer circles?
A. 3
B. 6
C. \(6\sqrt{2}\)
D. \(6\sqrt{3}\)
E. Cannot be determined
Are You Up For the Challenge: 700 Level Questions
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04 Jan 2021, 09:56
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A Hexagon is made up of 6 equilateral triangles.
The Radius of the circle is 1 and hence the side of the triangle is 2.
Area of Equilateral triangle = \(√3/4 × s^2\)
So the area of the 6 traingles that form this hexagon is 6 × √3/4 × 4
\(Area = 6√3\)
Answer (D)
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The Radius of the circle is 1 and hence the side of the triangle is 2.
Area of Equilateral triangle = \(√3/4 × s^2\)
So the area of the 6 traingles that form this hexagon is 6 × √3/4 × 4
\(Area = 6√3\)
Answer (D)
Posted from my mobile device
04 Jan 2021, 10:02
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The answer is D.
Since radius =1, therefore each side of the hexagon is 2. The formula for calculating the area of Hexagon is = {(3sqrt3)*(side)^2}/2 = {(3 sqrt 3)*(2)^2}/2 = 6*(sqrt 3)
Alternatively, the Hexagon can be viewed as 6 equilateral triangles with each side as diameter of the circle i.e. 2.... so area of 1 such triangle is (sqrt 3)/4 *(side)^2 = (sqrt 3)/4 *(2)^2 ... which is sqrt 3. Since there are 6 such triangles, So, the total area is = 6*(sqrt 3)... hope this is helpful.
Since radius =1, therefore each side of the hexagon is 2. The formula for calculating the area of Hexagon is = {(3sqrt3)*(side)^2}/2 = {(3 sqrt 3)*(2)^2}/2 = 6*(sqrt 3)
Alternatively, the Hexagon can be viewed as 6 equilateral triangles with each side as diameter of the circle i.e. 2.... so area of 1 such triangle is (sqrt 3)/4 *(side)^2 = (sqrt 3)/4 *(2)^2 ... which is sqrt 3. Since there are 6 such triangles, So, the total area is = 6*(sqrt 3)... hope this is helpful.
