In the above diagram, all the six line segments that extend from the

Question

Tough and Tricky questions: Geometry. 2014-12-24_1947.png In the above diagram, all the six line segments that extend from the center of the hexagon to the corners of the hexagon are 6 feet long, and the angle between each spoke is 60°. What is the perimeter of the hexagon? A. 36 B. 36√3 C. 72 D. 24√3 + 36 E. 36√3 + 24 Kudos for a correct solution .

pacifist85 · Answer

Is it A? Is there a trick I don't see here?

I used a circumscribed circles to cross-check it. I then drew a vertical line from the center of the circle on any of the sides of the hexagon. This line cut the 60 degree angle in two 30 degree angles. Then it created 2 smaller triangles. The angles of these smaller triangles have to have an angle of 30 degress (half the 60 degree angle), an angle of 90 degrees (where the vertical line falls) and another 60 degree angle (90+30=120 so 60 still left). So, the 6 triangles are all the same, with three 60 degree angles, which means that all of the sides are the same. So, A should be the answer. Right?

beattheheat · Answer

Each of the six triangles are equilateral with sides 6 feet long.
Perimeter = 6 * 6 = 36
Answer A

qw1981 · Answer

the angle between each spoke is 60 deg while each spoke are of equal length. This gives us a isosceles triangle with non equal angle of 60 degree. Thus it is an equliateral triangle. Same is the case with all the 6 triangles. Hence side of hexagon is 6.

Thus perimeter is 6*6=36 units. Answer is A.

Thus perimeter is 6*6=36 units. Answer is A.

Bunuel · Answer

OFFICIAL SOLUTION:

Each one of the formed triangles is isosceles, because two sides are equal (6 feet). An isosceles triangle with a 60⁰ angle is equilateral. All sides of an equilateral triangle are equal. Therefore all the sides of the hexagon equal 6 feet.A perimeter is the sum of all sides. P = 6 × 6 = 36.

The correct answer is A.

PareshGmat · Answer

Answer = A = 36

All the six small triangles formed are equilateral triangles.

Each of the side would be = 6

Perimeter = 6*6 = 36

In the above diagram, all the six line segments that extend from the

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In the above diagram, all the six line segments that extend from the

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