Question 1062790: A regular decagon is inscribed inside a circle. The circle has a radius of 6 units.
A: What is the approximate measure of the apothem of the decagon (rounded to the nearest hundredth of a unit)?
B: What is the approximate area of the decagon (rounded to the nearest whole square unit)?
Select only one answer each for parts A and B.
A: 3.71
A: 1.85
A: 5.71
A: 3.90
B: 111
B: 106
B: 113
B: 75
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Apothem=r cos (180/n), r=6 units
=6cos 180/10=6 cos 18=5.71 units, C.
1/2 the side is 6 sin 18=1.854 units
That makes the side 3.708 units, and the altitude is 5.71 units.
That product is 21.173 units. The area is 1/2 of that, and there are 10 such triangles in a decagon, so multiply 21.173*5=105.86. That rounds to 106 sq units or B.
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