SOLUTION: I have a hexagon and its side lengths are of 14cm, and it has a circular bulls eye right in the muddle with a diameter of 3cm. what is the probability that the dart that hits the

Question 37082This question is from textbook Geometry-reasoning applying measuring
: I have a hexagon and its side lengths are of 14cm, and it has a circular bulls eye right in the muddle with a diameter of 3cm. what is the probability that the dart that hits the target will hit the bulls eye?
Also it asks to estimate how many times a dart will the bulls eye if 100 darts hit the target? This question is from textbook Geometry-reasoning applying measuring

Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
The question asks you to compare the area of the circular bullseye to the area of the hexagon. The area of the hexagon is found by A = 1/2(a)(p) where a is the apothem and p is the perimeter. The apothem can be found by looking at the height of the equilateral traingles that make up a regular hexagon. It is 7 radical 3. So the hexagon's area is
A = (1/2)(7 radical 3)(84) = 294 radical 3 or about 509.2 sq cm.
The area of the bullseye is
A = (pi)r^2 = (1/4)(pi)d^2 = (9/4)(pi) or about 7.065 sq cm.
By dividing the two areas, we get 1.387% chance of hitting a bullseye if the arrows hit the target randomly. That means 1.387 arrows per hundred hit the bullseye.
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