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11.4 Circumference and Arc Length . Learning Target: I can use similarity to calculate the length of an arc. . **. Review:. Interior angles of a polygon Find the sum of the measures of the interior angles of a convex 20-gon. Sum of interior angles = (n – 2) · 180°

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## 11.4 Circumference and Arc Length

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**11.4 Circumference and Arc Length**Learning Target: I can use similarity to calculate the length of an arc.******Review: Interior angles of a polygon • Find the sum of the measures of the interior angles of a convex 20-gon. Sum of interior angles = (n – 2) · 180° = (20 – 2) · 180° = (18) · 180° = 3240°**Circumference of a Circle**• The circumference ( C ) of a circle is • C = πd or • C = 2πr where d = diameter of the circle and r = radius of the circle.******Example: (a) Find the circumference of a circle with radius 6cm (b)Find the radius of a circle with circumference 31m. Circumference = 2πr C = 2π(6) C=12π Circumference = 2πr 31 = 2πr r ≈ 4.9**Arc Length Corollary**In a circle, the ratio of the length of a given arc to the circumference is equal to the ratio of the measure of the arc to 360°. Arc length of AB =**.**C A 50° 5 . 7 50° D B Find the length of each arc.**P**. 3.82 60° Q R Find the circumference. Circumference = 2πr**Find the circumference.**Circumference = 2πr

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