SOLUTION: Find the area of the regular 15-gon with radius 9 mm

Question 1154051: Find the area of the regular 15-gon with radius 9 mm
Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Find the area of the regular 15-gon with radius 9 mm
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It's 15 isosceles triangles, each with a central angle of 360/15 = 24 degs.
---> 30 right triangles with a hypotenuse of 9 mms and a smallest angle of 12 degs.
base b = 9*cos(12)
Height h = 9*sin(12)
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The area of each triangle is b*h/2

Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

≈

or this way:

View post on imgur.com

Observe that m < , as there are congruent triangle around
and m <
if , m <

The sides of that triangle are:
,

and area of the triangle is:

then double it to get area of the isosceles triangle :

the area of the regular 15-gon is:

Therefore area of the regular 15-gon with radius is ≈

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