Find the area of the Hexagon.
Given:
Apothem 7
90 degree angle is formed by the apothem and side.
The perimeter is not given nor the length of the sides
2007-02-13 02:52:38 · 7 answers · asked by Nelly 2 in Science & Mathematics ➔ Mathematics
Is it a regular hexagon? I suppose so, otherwise we wouldn't be talking about "the" apothem.
So... take A = a vertex, B = the intersection of the apothem and side, and C = the center of the hexagon, then ABC is a 30-60-90 triangle. Solve this triangle - the hexagon contains 12 of them.
2007-02-13 02:59:22 · answer #1 · answered by Anonymous · 0⤊ 0⤋
The area given by A= perimeter *apothem /2 .In an hexagon
there are six eqilateral triangles and the apothem is just the height of any one.
As you know the height of an equilateral triangle is = = side *(sqr3)/2= apothem so side = 2*apothem /sqrt3=
2*sqrt3*apothem/3 and the perimeter = 4sqrt3*apothem
So the area is 2*sqrt3(apothem)^2 = 98 sqrt3
2007-02-13 03:06:15 · answer #2 · answered by santmann2002 7 · 0⤊ 0⤋
Cut the hexagon into 8 triangles. Each triangle has a point at the center of the hexagon, and the base of the triangle is a side of the hexagon.
360 / 8 = 45, ... that's the angle inside each tip of the triangles.
The other 2 angles are equal, and the sum of 3 angles must be 180 degrees.
So the angles of each triangle are 45 degrees, 67.5 degrees, and 67.5 degrees.
You are given the height of the triangle: 7 units.
The base of the triangle is 2 * (7 / tan(67.5 deg)) =
Area of each triangle = height * base /2
There are 8 triangles, so take the area of one, and multiply by 8.
2007-02-13 03:07:22 · answer #3 · answered by morningfoxnorth 6 · 0⤊ 0⤋
opposite 60 degree angle = 7
opposite 30 = 7/sq rt 3 = 7 sq rt 3 / 3
each side is 14 sq rt 3 / 3 Perimeter is 28 sq rt 3
A = 1/2 a p = 1/2 (7) (28 sq rt3) = 98 sq rt 3
2007-02-13 02:57:00 · answer #4 · answered by richardwptljc 6 · 0⤊ 0⤋
No, you're not missing anything.
You can calculate the length of the sides from the apothem.
2007-02-13 02:56:40 · answer #5 · answered by Stu 2 · 0⤊ 0⤋
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2016-12-17 09:03:15 · answer #6 · answered by ? 4 · 0⤊ 0⤋
if apothem is given
rt3/2 a=7
a=14/rt3
area=(3a)(7)
3*14/rt3*7
rationalising
area=294rt3/3 sq.units
=98rt3 sq.units
2007-02-13 03:01:24 · answer #7 · answered by raj 7 · 0⤊ 0⤋