Question 141814This question is from textbook
: how do you find the area of a regular pentagon with radius 10cm?
This question is from textbook
Answer by edjones(8007)   (Show Source):
You can put this solution on YOUR website! r=10, s=side length, n=number of sides, A=area
For any regular polygon: r=s/(2sin(pi/n)) using radians.
10=s/(2sin(pi/5))
10=s/1.17557...
s=11.76...
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Heron's Law:
Let a=10, b=10, c=11.76
s=(a+b+c)/2 Don't confuse this s with the s above which is now c. This is a new s.
=(10+10+11.76)/2
=15.88...
A=sqrt(s(s-a)(s-b)(s-c)) Area of the triangle
=sqrt(15.88(15.88-10)(15.88-10)(15.88-11.76))
=47.56
47.56*5=237.8 cm^2 Area of the pentagon.
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Ed
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