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Areas of Regular Polygons

Areas of Regular Polygons. Objective : To find the areas of regular polygons. Definition: Regular Polygon. an equilateral and equiangular polygon. Regular polygon- ___________________ _______________________________________. Area ∆ = ____________.

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Areas of Regular Polygons

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  1. Areas of Regular Polygons Objective:To find the areas of regular polygons Geometry

  2. Definition: Regular Polygon an equilateral and equiangular polygon Regular polygon-___________________ _______________________________________ Geometry

  3. Area ∆ = ____________ KEYFinding areas of irregular polygonal regions: • Divide the irregular region into familiar geometric regions. • Determine individual areas. • Add to determine total area. Geometry

  4. Divide the polygon on the LEFT into familiar geometric regions. • Divide the polygon into isosceles ∆s. • Find the area of each triangle. • Add to determine the total area. height (apothem) Base (side) Geometry NOTE: Each region is an isosceles ∆.

  5. Regular Polygon Area Theorem Area ∆ = ½ bh = ½ sa Area (reg. poly.) = ½ as n*, where n is the number of sides. The area of a regular polygon is given by the formula __________________, where A is the Area, a is the apothem, s is the length of a side, and n is the number of sides of the regular polygon. Since the length of each side times the number of sides (sn) is the _______________, the formula can also be written ____________. A = ½ asn perimeter A = ½ ap Geometry

  6. Decisions, Decisions, Decisions… NOTE: When a problem gives you (or asks you to find the perimeterof a regular polygon, use ______________. NOTE: When a problem gives you (or asks you to find the length of a sideof a regular polygon, use _____________. A (reg. poly.) = 1/2 ap A (reg. poly.) = 1/2 asn Geometry

  7. Determine which area formula to use. Explain (underlineKEY words). • Pentagon; a ≈ 3 cm and s ≈ 4.4 cm A = __________ • Decagon; a ≈ 9.7 cm and s ≈ 14.1 cm A = __________ • Octagon; a ≈ 12.1 cm and p ≈ 80 cm A = __________ • Nonagon; p ≈ 63 cm and a ≈ 9.6 cm A = __________ Geometry

  8. Determine which area formula to use. Explain (underlineKEY words). • Find the area of a regular polygon with a ≈ 12 cm and p ≈ 81.6 cm. A = __________ 6) Find the perimeter of a regular polygon to the nearest tenth of a meter if a a ≈ m and A ≈ 259.2m2. A = __________ 7) Find the length of each side of a regular polygon to the nearest foot if a ≈ 80 ft., n = 20, and A ≈ 20,000 square feet. A = __________ Geometry

  9. Final Checks for Understanding • Use your new theorem to find the area of a regular polygon accurate to the nearest square centimeter. • Find the area of a regular heptagon if the apothem is 3.2m in length and the length of a side is 4m. • Find the perimeter of a regular polygon if the apothem is 7cm in length and the area = 182cm2. Geometry

  10. Homework Assignment: Areas of Regular Polygons WS Geometry

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