Answer:
74.46
Step-by-step explanation:
There is another problem exactly like this one, except for the fact that it askes for the white area. The answer there is 25.54%, so it will be 74.46% here. I can't explain the actual reasoning unfortunately.
The probability that a randomly selected point within the circle falls in the red-shaded area is 75.61%.
It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
It is given that:
The radius of the circle r = 4 cm
The area of the circle A = πr²
A = π(4)²
A = 16π square cm
The total number of outcomes = 16π square cm = 50.26 square cm
The side length of the pentagon a = 4.7 cm
The area of the pentagon can be calculated using:
Area = (1/4)√[5(5+2√5)]a²
Plug a = 4.7
Area = (1/4)√[5(5+2√5)](4.7)²
After calculating:
Area = 38.01 square cm
Total favorable outcomes = 38.01 square cm
The probability = 38.01/50.26
The probability = 0.7561
In percent:
The probability = 75.61%
Thus, the probability that a randomly selected point within the circle falls in the red-shaded area is 75.61%.
Learn more about the probability here:
brainly.com/question/11234923
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