I'm not a math person and couldn't figure out how to answer this question even if you explained it to me. (I've asked this question before and got a lot of detailed answers about how to solve the problem, but I'm looking for a solution to a real-world problem and just need the answer itself.)
I have a regular hexagon that is 12 feet across (side to side, not point to point).
How many many square feet are contained in that hexagon?
2007-07-20 15:32:51 · 4 answers · asked by N C 1 in Science & Mathematics ➔ Mathematics
Sorry to say, but the first two answers are incorrect.
The area of your hexagon is 124.71132 square feet.
Since we are discussing a regular hexagon, we are dealing with six identical triangles. If lines are drawn across opposite vertices we have six identical equilateral triangles. Agreed? Since we are dealing with a regular hexagon the central angles formed by the diagonals are 60 degrees. Thusly the other two angles in each triangle are also 60 degrees.
That having been said we only need find the area of one of the triangles and multiply that area by 6. The height (altitude) of one of those triangles is 6 which is half of the 12 foot dimension, side to side. Since we are working with an equilateral triangle the altitude splits the triangle into two 30-60-90 triangles. The base of each of the 30-60-90 triangles is 6/sqrt3. The area of each equilateral triangle is therefore is 36/sqrt3........the area of the entire hexagon is 216/sqrt3. The area of the hexagon is 124.71132 square feet.
2007-07-20 16:16:48 · answer #1 · answered by popcorn 3 · 0⤊ 0⤋
If I read your question right, "I have a regular hexagon that is 12 feet across (side to side, not point to point)", then the first two answers were incorrect. If the side to side width is 12 feet, the sides of the hexagon are 4sqrt3 feet long. Unfortunately they are not a nice number, but irrational. 4sqrt3 is about 6.93 feet or 6 feet 11 inches. I say about because the sqrt3 is non-ending and non-repeating so it will not be exact. This means your area is 72*sqrt3 or about 124.7 feet. This is 124 feet 8 and one half inches. 124 ft, 8 1/2 in. I hope this helps.
2007-07-20 15:53:58 · answer #2 · answered by Steven R 1 · 0⤊ 0⤋
You need to measure point to point. Not side to side. The formula works when you can split the hexagon into equilateral triangles.
The formula for the area of a regular hexagon can be stated as ((3*sqrt3)/2) * x^2 or, to simplify, approximately 2.598076211 * x^2.
I did this for a point to point 12 foot triangle. There might not be much difference in the area but its not the same as side to side.
x is the length of each side. If the diametre is 12 feet and you dived the hexagon into 6 equilateral triangles then each side equals 6 feet. Just plug in 6 for x and you have your area.
6^2 = 36
36 * 2.598076211 = about 93.530743596 square feet.
2007-07-20 15:37:45 · answer #3 · answered by Lady Geologist 7 · 0⤊ 1⤋
For this type of problem, you cannot use the normal formula of a regular hexagon. Consider that the given length is a "diameter".
The area of any regular polygon is:
A = n * sin (180/n) * cos (180/n) * r^2
... where n = number of sides, and r = radius.
For the hexagonal problem, n = 6 and r = 6 (half of 12 feet)
Therefore:
A = 6 * sin (180/6) * cos (180/6) * 6^2
A = 6 * sin 30 * cos 30 * 36
A = 93.53 sq. ft.
2007-07-20 15:38:26 · answer #4 · answered by pisayweb 3 · 0⤊ 1⤋