1. Mrs. McConaughyGeometry1 Areas of Regular Polygons Objective: To find the areas of regular polygons

2. Mrs. McConaughyGeometry2 Regular polygon- ___________________ _______________________________________ Definition: Regular Polygon an equilateral and equiangular polygon

3. Mrs. McConaughyGeometry3  Divide the irregular region into familiar geometric regions.  Determine individual areas.  Add to determine total area. KEY Finding areas of irregular polygonal regions: Area ∆ = ____________

4. Mrs. McConaughyGeometry4 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. NOTE: Each region is an isosceles ∆. height (apothem) Base (side)

5. Mrs. McConaughyGeometry5 Regular Polygon Area Theorem 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 Area ∆ = ½ bh = ½ sa Area (reg. poly.) = ½ as n*, where n is the number of sides.

6. Mrs. McConaughyGeometry6 Decisions, Decisions, Decisions… NOTE: When a problem gives you (or asks you to find the perimeter of a regular polygon, use ______________. NOTE: When a problem gives you (or asks you to find the length of a side of a regular polygon, use _____________. A (reg. poly.) = 1/2 a s n A (reg. poly.) = 1/2 a p

7. Mrs. McConaughyGeometry7 Determine which area formula to use. Explain (underline KEY words). 1.Pentagon; a ≈ 3 cm and s ≈ 4.4 cm A = __________ 2.Decagon; a ≈ 9.7 cm and s ≈ 14.1 cm A = __________ 3.Octagon; a ≈ 12.1 cm and p ≈ 80 cm A = __________ 4.Nonagon; p ≈ 63 cm and a ≈ 9.6 cm A = __________

8. Mrs. McConaughyGeometry8 Determine which area formula to use. Explain (underline KEY words). 5)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 = __________

9. Mrs. McConaughyGeometry9 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 = 182cm 2.

10. Mrs. McConaughyGeometry10 Homework Assignment: Areas of Regular Polygons WS