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
:
each angle is 360/5 = 72 degrees
:
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.
:
angle AOB is 72/2 = 36 degrees and angle AOB is 36/2 = 18 degrees
:
for triangle AOB, we have
:
36 +18 +Beta = 180
:
Beta = 180 -36 -18 = 126 degrees
:
radius of circle = 20/2 = 10 cm
:
Now use the law of sines
:
(OB/sin(18)) = (10/sin(126))
:
OB = 10 * sin(18) / sin(126)
:
OB = 3.8197
:
Area of triangle AOB = (1/2) * 3.8197 * 10 * sin(36) = 11.2258
:
Area of the five pointed star = 10 * 11.2258 = 112.258 square cm's
:
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