I'm trying to find the area of a regular hexagon with 14 foot sides. I realize that I need to calculate A = .5aP, but I don't know how to find the apothem. Help?
2006-09-22 03:35:58 · 7 answers · asked by Anonymous in Education & Reference ➔ Homework Help
To find apothem r, r = z / 2 tan (pi/n) where z = length of a side, n = number of sides.
r = 14 / 2 tan (pi/6)
r = 14 / 2 * 0.577 (remember, use radians instead of degrees)
r = 14 / 1.154
r = 12.131 ft
2006-09-22 03:43:42 · answer #1 · answered by ³√carthagebrujah 6 · 0⤊ 0⤋
When you draw the apothem to a side of the hexagon, you form a right triangle and the apothem bisects that side. Since the radius of the regular hexagon is the same length as a side, the radius = 14. Your right triangle formed has one leg = 7 and the hypotenuse = 14. It so happens the right triangle is a 30-60-90 right triangle and 7 is the shorter leg, you can find the longer leg (apothem) by dividing 7 by sqrt(3), or you could use the Pythagorean theorem. Your choice. And that's how you can get the length of the apothem in a regular hexagon.
2006-09-22 05:08:14 · answer #2 · answered by LARRY R 4 · 0⤊ 0⤋
I have no idea what an apothem is but since it is a hexagon, you could draw three lines making three equilateral triangles with each having two sides of the original hexagon. and leaving you with a further equilateral triangle in the centre. So then the area would be = 4 x area of equilateral triangle of side 14 ft.
= 4 x sqr root 3 x (14 /2 ) x (14/ 2)
= 196 x 1.732 = approx339.5 sq ft.
2006-09-22 03:46:58 · answer #3 · answered by jazideol 3 · 0⤊ 0⤋
Connect the six vertices's of the regular hexagon to its center, creating 6 equilateral triangles whose sides are 14 foot. Thus the area of a regular hexagon, whose sides have length 14 foot, is 6 times the area of a equilateral triangles whose sides are 14 foot.
2006-09-22 03:48:48 · answer #4 · answered by Anonymous · 0⤊ 0⤋
right here is yet differently to sparkling up the priority. amplify a area and form an outdoors perspective. then you incredibly undergo in concepts the sum of the outdoors angles is often 360 ranges. Now divide by potential of 5 via fact there are 5 factors which promises you seventy two. Now the interior perspective is supplementary to the outdoors perspective, so a hundred and eighty - seventy two = 108 ranges. word: This technique will purely artwork for favourite polygons.
2016-12-18 14:53:27 · answer #5 · answered by Anonymous · 0⤊ 0⤋
2+2=3 Ha! only if my math teacher Mr. Freidman could see me now.
2006-09-22 03:38:23 · answer #6 · answered by prizelady88 4 · 0⤊ 1⤋
Geometry is not my strong point.
It might be yours if you can figure this out yourslef.
2006-09-22 03:45:42 · answer #7 · answered by nia93me 2 · 0⤊ 0⤋