SOLUTION: In a circle with diameter of 12 inches, a regular five-pointed star is inscribed. What is the area of that part not covered by the star? Answer: 72.68 square inches

Algebra ->  Surface-area -> SOLUTION: In a circle with diameter of 12 inches, a regular five-pointed star is inscribed. What is the area of that part not covered by the star? Answer: 72.68 square inches      Log On


   

Question 1117223: In a circle with diameter of 12 inches, a regular five-pointed star is inscribed. What is the area of that part not covered by the star?
Answer: 72.68 square inches
Answer by math_helper(2461) About Me  (Show Source):
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Area of circle is +pi%2Ar%5E2+=+pi+%2A+6%5E2+=+36%2Api+ or about 113.0973 sq in.

Area of regular 5-pointed star is ++%2810tan%28pi%2F10%29+%2F+%283-tan%5E2%28pi%2F10%29%29+%29+r%5E2+ approx = +10%2A%280.32492%29%2F%283-%280.32492%5E2%29%29%2A36+=+40.4125+ sq in

Subtract the area of the star from that of the circle to get 113.0973 - 40.4125 = 72.6848 sq in