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Calculating Areas of Regular Polygons

Explore how to find the area of regular polygons using side length, apothem, and central angles. Practice with various polygon examples.

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Calculating Areas of Regular Polygons

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  1. Unit 9 Lesson 5 – Areas of Regular Polygons

  2. Center of a polygon: Point equidistant to the vertices of the of the polygon P

  3. Radius of a polygon: Length from the center to the vertex of a polygon

  4. Apothem of the polygon: Length from the center to the side of a polygon

  5. Central angle of a regular polygon: Angle formed by two radii in a polygon

  6. 1. Find the measure of a central angle of a regular polygon with the given number of sides. Round answers to the nearest tenth of a degree if necessary. 6 sides 60° 60°

  7. 1. Find the measure of a central angle of a regular polygon with the given number of sides. Round answers to the nearest tenth of a degree if necessary. 12 sides 30°

  8. 1. Find the measure of a central angle of a regular polygon with the given number of sides. Round answers to the nearest tenth of a degree if necessary. 40 sides 9°

  9. 1. Find the measure of a central angle of a regular polygon with the given number of sides. Round answers to the nearest tenth of a degree if necessary. 21 sides 17.1°

  10. 2. Find the given angle measure for the regular hexagon shown. Each central angle = 60° 60° mEGF = 60° mEGD = 60°

  11. 2. Find the given angle measure for the regular hexagon shown. mEGH = 30° 60° 30°

  12. 2. Find the given angle measure for the regular hexagon shown. mDGH = 30° 60° 30° 30°

  13. 2. Find the given angle measure for the regular hexagon shown. mGHD = 90°

  14. Area of a regular polygon: s = side length a = apothem length n = number of sides

  15. 3. A regular pentagon has a side length of 8in and an apothem length of 5.5in. Find the area.

  16. 4. Find the area of the polygon. 42 = a2 + 22 16 = a2 + 4 12 = a2 Apothem = _____________ A = ____________________

  17. 5. Find the area of the polygon. c2 = a2 + b2 6.82 = a2 + 42 46.24 = a2 + 16 30.24 = a2 5.5 5.5 = a 5.5in Apothem = _____________ A = ____________________

  18. 6. Find the area of the polygon. 120° 60° 60° 30° 12cm 12cm 24cm 120° mACB = _______ Apothem = ___________ A = __________________

  19. 6. Find the area of the polygon. 2 1 30° 12cm 12cm  120° mACB = _______ Apothem = ___________ A = __________________

  20. 6. Find the area of the polygon. 12cm 12cm 120° mACB = _______ Apothem = ___________ A = __________________

  21. 7. Find the area of the polygon. 60° 30° 60° 5m 5m 60° mACB = _______ Apothem = ___________ A = __________________

  22. 30° 5m 5m 7. Find the area of the polygon. 2 1 60° 60° mACB = _______ Apothem = ___________ A = __________________

  23. 30° 5m 5m 7. Find the area of the polygon. 60° mACB = _______ Apothem = ___________ A = __________________

  24. 8. Find the area of the polygon. 72° 36° 72° mACB = _______ Side Length = ________ A = __________________

  25. 8. Find the area of the polygon. SOH – CAH – TOA 36° 1 H A 15.98 = x 15.98 15.98 O 72° mACB = _______ 31.96cm Side Length = ________ A = __________________

  26. Find the area of the polygon. 36° H A 15.98 15.98 O 72° mACB = _______ 31.96cm Side Length = ________ A = __________________

  27. 9. Find the area of the polygon. 45° 22.5° 45° mACB = __________ Apothem = __________ Side Length = ________ A = __________________

  28. 9. Find the area of the polygon. SOH – CAH – TOA 1 H A 22.5° 5.54 5.54 = a 2.3 2.3 O 45° 1 mACB = __________ Apothem = __________ Side Length = ________ A = __________________ 5.54in 4.6in 2.3 = x

  29. 9. Find the area of the polygon. H A 22.5° 5.54 2.3 O 2.3 45° mACB = __________ Apothem = __________ Side Length = ________ A = __________________ 5.54in 4.6in

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