Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Each regular polygon has radii and apothem as shown. Find the measure of each numbered angle.

See Problem 2.

Find the area of each regular polygon with the given apothem a and side length s.

11. pentagon, a = 24   . 3   cm , s = 35   . 3   cm eh equals 24 . 3 cm comma . s equals 35 . 3 cm
12. 7-gon, a = 29   . 1    ft , s = 28    ft eh equals 29 . 1 ft comma . s equals 28 ft
13. octagon, a = 60   . 4   in. , s = 50   in. eh equals 60 . 4 in. comma . s equals 50 in.
14. nonagon, a = 27   . 5   in. , s = 20   in. eh equals 27 . 5 in. comma . s equals 20 in.
15. decagon, a = 19   m , s = 12   . 3   m eh equals 19 m comma s equals 12 . 3 m
16. dodecagon, a = 26   . 1   cm , s = 14   cm eh equals 26 . 1 cm comma . s equals 14 cm

See Problem 3.

Find the area of each regular polygon. Round your answer to the nearest tenth.

17. 
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20. Art You are painting a mural of colored equilateral triangles. The radius of each triangle is 12.7 in. What is the area of each triangle to the nearest square inch?

    

Find the area of each regular polygon with the given radius or apothem. If your answer is not an integer, leave it in simplest radical form.

B Apply

Find the measures of the angles formed by (a) two consecutive radii and (b) a radius and a side of the given regular polygon.

26. pentagon
27. octagon
28. nonagon
29. dodecagon

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