Suppose a circle of radius r is inscribed in a hexagon. Find the area of the hexagon.
2007-11-05 13:41:48 · 7 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
assuming that your hexagon is a regular hexagon, the area of the hexagon will equal 6 triangles, with the length of all three sides of each of these triangles the radius r of the circle.
2007-11-05 13:44:36 · answer #1 · answered by You'll Never Take Me Alive!! 3 · 0⤊ 0⤋
Pardon some arm-waving, but if a cirlce is inscribed inside a hexagon, the radius is perpendicular bisector of a side where the circle is tangent to the hexagon. If you call one such side AB and the radius OC, then AC=AB and AOC is a 60/30/90 right triangle. You have 12 of these in the hexagon. The opposite sides of such a triangle are in the ratio of sqrt(3),1, 2. In this case, r corresponds to the sqrt(3) in the ratio, so AC, the side opposite the 30 deg angle is length r/sqrt(3) or (r/3)sqrt(3). Since area= bh/2, the area of AOC is (r/2)*(r/3)sqrt(3). Multiplying this by 12, we get 2r^2 sqrt(3) as the area.
2007-11-05 13:58:21 · answer #2 · answered by cattbarf 7 · 0⤊ 0⤋
Hexagon is made up of 6 triangles with height equal to the radius of the circle and base equal to 2r tan(30), So the area of the hexagon is 6 x 1/2 b x h
= 6 x 1/2 x r x 2 r tan(30)
2007-11-05 13:48:57 · answer #3 · answered by Anonymous · 0⤊ 0⤋
the area of a time-honored hexagon (could be time-honored to have a circle inscribed in it) is A = a million/2 * apothem * perimeter The apothem is the area from the midsection to a minimum of one facet. for this reason, the apothem is = radius of the circle. the fringe of a hexagon is 4?3 * apoothem, so A = a million/2 * r * 4?3 * r = 2?3 * r^2
2016-10-03 10:51:06 · answer #4 · answered by ? 4 · 0⤊ 0⤋
Think about how you can use the radius of the circle to determine the dimensions of the hexagon.
Do you know how to calculate the area of a triangle? Is there any way you can use that knowledge to help you calculate the area of the hexagon?
2007-11-05 13:45:15 · answer #5 · answered by mdd4696 3 · 0⤊ 0⤋
we assume it is a regular hexagon.
then you know that the distance from center of one of the sides of the hexagon to the center point of the figure is r. use simple geometric or trigonmetric relationships to find the area.
2007-11-05 13:44:50 · answer #6 · answered by Anonymous · 0⤊ 0⤋
not going to be original on this one ... see the site below, the only difference is that in this case they set r=1. (did not check it was correct).
2007-11-05 13:51:54 · answer #7 · answered by Anonymous · 0⤊ 0⤋