If a hexagon is 12 feet in diameter, how many square feet are contained therein?
2007-07-20 10:27:20 · 4 answers · asked by N C 1 in Science & Mathematics ➔ Mathematics
A = ((3/sqrt 3)/2) * x^2 or approximately 2.598076211 * x^2
x = length of the side which in your case if it is a regular hexagon and the diametre is 12 feet the sides are 6 feet.
2007-07-20 10:34:12 · answer #1 · answered by Lady Geologist 7 · 0⤊ 0⤋
I got 76.3675 (rounded)
The perimeter was 36 (each side was 6)
The apothem was 3 square root of 2.
Since A = 1/2 Pa, A = 1/2 (36)(3 square root of 2)
Here's how I got those answers.
Since the diameter was 12, the radius was 6. Next, to find angle measures in the right triangle that is formed inside the hexagon, I took (360/6)/2 to find that the top angle is 30 degrees. This makes a 30-60-90 triangle, and with a hypotenuse of 6, you get an apothem of 3 square root of 2 and a base of 3. Double the base to find the length of the side (6) and multiply be 6 to find the perimeter (36).
2007-07-20 10:42:14 · answer #2 · answered by Anonymous · 0⤊ 0⤋
Every side of this hexagon is 12. Cut the hexagon into six equilateral triangles. The area of each triangle is root 3 x s/4. There are six triangles, so 6x3x root 3 =18 root 3.
2007-07-20 10:49:14 · answer #3 · answered by yoo 2 · 0⤊ 0⤋
tricky step. do a search onto search engines like google. it can help!
2014-12-05 15:51:35 · answer #4 · answered by ? 3 · 0⤊ 0⤋