SOLUTION: In a circle with diameter of 20 cm, a regular five-pointed star touching its circumference is inscribed.Find the area of the star.
Answer: 112.267 sq cm
Need solution.
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-> SOLUTION: In a circle with diameter of 20 cm, a regular five-pointed star touching its circumference is inscribed.Find the area of the star.
Answer: 112.267 sq cm
Need solution.
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Question 1117226: In a circle with diameter of 20 cm, a regular five-pointed star touching its circumference is inscribed.Find the area of the star.
Answer: 112.267 sq cm
Need solution. Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website! there are 5 central angles
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each angle is 360/5 = 72 degrees
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label a point of the star on the circumference A, center of the circle O and the intersection of the side of A and the side of the point of the star adjacent to A going clockwise B.
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angle AOB is 72/2 = 36 degrees and angle AOB is 36/2 = 18 degrees
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for triangle AOB, we have
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36 +18 +Beta = 180
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Beta = 180 -36 -18 = 126 degrees
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radius of circle = 20/2 = 10 cm
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Now use the law of sines
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(OB/sin(18)) = (10/sin(126))
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OB = 10 * sin(18) / sin(126)
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OB = 3.8197
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Area of triangle AOB = (1/2) * 3.8197 * 10 * sin(36) = 11.2258
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Area of the five pointed star = 10 * 11.2258 = 112.258 square cm's
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