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Ch. 10.5 Regular Polygons

Polygon – Closed plane figure formed from three or more segments, each of which intersect exactly two other segments at their endpoints. Polygons. Not Polygons. Ch. 10.5 Regular Polygons. Types of polygons. Convex polygon. Concave polygon. All angles open in. At least on angle opens out.

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Ch. 10.5 Regular Polygons

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  1. Polygon – Closed plane figure formed from three or more segments, each of which intersect exactly two other segments at their endpoints. Polygons Not Polygons Ch. 10.5 Regular Polygons

  2. Types of polygons Convex polygon Concave polygon All angles open in At least on angle opens out

  3. ) ) ) Regular Polygon – A polygon whose sides are congruent and angles are congruent. 60 Every regular polygon has a center. Center: point D 60 60 The center is equidistant (same distance) from each side and vertex. DG = DF = DE DC = DB = DA

  4. Apothem - Segment drawn from the center of a regular polygon  (perpendicular) to a side.

  5. 2) Find the area of ABCDEF 1) Find the area of ABC 24 in 18 cm 5.19 20.8 DE = 5.19 cm GH = 20.8 A = 1497.6 in2 A = 140.13 cm2

  6. Perimeter of a regular polygon Area of a regular polygon

  7. 1) Find the area of a regular triangle if the apothem is 9 in and each side measures 31.2 in. A = 421.2 in2 2) Find the area of a regular pentagon if the apothem is 13.8 cm and each side measures 20 cm. A = 690 cm2 3) If each side of a regular nonagon measures 32 ft and the apothem is 44 ft, what is the area? A = 6336 ft2 4) What is the area of a regular 12-gon if each side is 10.2 ft and the apothem is 19 ft? A = 1162.8 ft2

  8. 5) The area of a regular polygon is 1039.2 ft2. If each side is 20 ft and the apothem is 17.32 ft, how many sides does the polygon have? sides = 6 6) Find the length of the apothem of a regular pentagon if each side measures 23.2 cm and the area is 928 cm2. apothem = 16 7) The area of a regular octagon is 4344 in2. Find the length of each side if the apothem is 36.2 in. side = 30

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