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1) measure of a central angle =....
2) apothem =...
3) radius =...
4) area =...

2007-04-21 06:49:58 · 3 answers · asked by Anita K 1 in Science & Mathematics Mathematics

3 answers

1) 360/6 = 60 degrees
2) side/2*sqrt(3) = 9sqrt(3) units
3) radius = side = 18 units
4) A = aP/2 = 9sqrt(3)(6)(18) /2= 486sqrt(3) units^2

2007-04-21 06:57:00 · answer #1 · answered by ironduke8159 7 · 0 0

central angle is 360°/6 = 60°

apothem = 9√3 (use 30-60-90 triangle relationship)

radius = 18 because the triangles formed when you draw all the radii are equilateral, so they have sides the same as the side of the hexagon

For area, you have two options. The formula most geometry books give for regular polygons is .5*apothem*perimeter. But specifically for regular hexagons, you can use 6 equilateral triangles and never have to find the apothem or perimeter. It would be 6(s²√3 / 4) = 3s²√3 / 2 where s is the side of the hexagon.

A = 3*18² *√3 / 4 = 243√3

2007-04-21 07:24:10 · answer #2 · answered by Kathleen K 7 · 0 0

Regular Polygon Formulas

The Regular Hexagon

Number of sides n = 6
Internal angles beta = 2pi/3 radians = 120 degrees
Central angles alpha = pi/3 radians = 60 degrees

Perimeter P = 6a = 6R
Area K = 3a2 sqrt(3)/2
= 3R2 sqrt(3)/2
= 2r2 sqrt(3)
= 3a sqrt(4R2-a2)/2

Circumradius R = a
Apothem r = a sqrt(3)/2 = R sqrt(3)/2

Side a = 2r/sqrt(3) = R

2007-04-21 07:08:52 · answer #3 · answered by Anonymous · 0 0

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