Regular Polygon
A regular polygon with sides measuring 2.8cm has an area of 103.38cm^2. Determine the number of the diagonals of the polygon
Homework Answers
Total area 103.38 divided by n is area of each triangle. This is also equal to 1.4h. We know that tan(theta)=1.4/h. Therefore h can be rewritten as 1.4/tan(theta). Substitute.
Now we can say that 103.38(tan(theta))=1.4^2(n)
We also know 360/2theta = n
We're left with a simplified equation:
theta(tan(theta))=3.413 (very close to 2+sqroot2), basically y=xtanx.
We can plot this and arrive at theta=13.85 degrees
So 360/2*13.85=13 sides
That was the hard part.
The number of diagonals is n(n-3)/2=65.
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//include comments
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//include comments
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