2007-05-20 16:53:02 · 6 answers · asked by Sam J 1 in Science & Mathematics ➔ Mathematics
alright
A regular hexagon has 6 equilateral triangles
so consider one triangle.. multply the area by 6
and u have the area of a regular hexagon.
The area of each equilateral triangle is about
2.51 cm^2.
multiply that times 6 and the answer is 15.1 cm^2
BTW area of a triangle is .5 b h ..
b is 1.5 and height is sqrt 11.25
2007-05-20 16:58:48 · answer #1 · answered by sudhi_kandi 3 · 0⤊ 0⤋
Draw a hexagon on a piece of paper. Draw a straight line from its right side to the left to make a diameter. Now the hexagon is divided into two parts. Now divide the upper and the lower parts into 6 equilateral triangles. So now you have 6 equilateral triangles with each side equal to 3 centimeters.
The diameter of the hexagonal is equal to 6 if you look at our triangles so half the diameter is 3 for the height of each triangle.
Now if you calculate the area of one of the triangles using the formula:
½ * b * h
Where:
b : is the base which for us is 3 centimeters.
h : is the height which again is 3 centimeters.
So the area of one of triangles is:
½ * 3 * 3 = ½ * 9 = 4.5
Since we have 6 of these triangles in our hexagonal, multiply the area of 4.5 by 6 to get: 27. The area of the hexagonal is 27.
2007-05-20 17:02:22 · answer #2 · answered by ¼ + ½ = ¾ 3 · 0⤊ 0⤋
if the component has length 10 cm, the apothem is 5 sqrt(3) cm the hexagon could be drawn as 12 suited triangles each and each with height = 5 and length = apothem A = 12 (25/2) sqrt(3) = 259.8076 cm^2
2016-12-11 15:29:33 · answer #3 · answered by ? 4 · 0⤊ 0⤋
Draw the picture.
The hexagon can be divided into six 60º,60º,60º triangles.
The area of each is (1/2)(base)(height). Each has a base of 3 centimeters. The height is not 3 cm. The height is [(3/2)√3]cm.
Area of equilateral triangle = (1/2)(3cm)(3/2)(√3)cm = [(9√3)/4]cm².
The hexagon area is 6 times that = [(54√3)/4]cm² = [13.5√(3)]cm².
2007-05-20 17:20:47 · answer #4 · answered by Mark 6 · 1⤊ 0⤋
FROM intense geometrical analysis, The area of any regular hexagon given its side length of m centimeters is
2 x h (3b/2) where h= (b/2)sqrt(3) or simplifying:
2.61 b^2
2007-05-20 17:07:38 · answer #5 · answered by cattbarf 7 · 0⤊ 0⤋
its 27.
trick in solving geometric problems: divide the polygon into triangles
2007-05-20 17:10:49 · answer #6 · answered by eucca 2 · 0⤊ 0⤋