Name _____ Date Period HW – Areas of Regular Polygons In a regular polygon, a segment drawn from the center of the polygon perpendicular to a side of the polygon is called an apothem. In the figure at the right, PS is an apothem. If a regular polygon has an area of A square units, a perimeter of P units, and an apothem of a units, then A = or A = Example: Find the area of a regular pentagon with an apothem of 2.8 cm and a perimeter of 20.34 cm. A = Area of a regular polygon A = (20.34)(2.8) A = 28.476 The area is 28.476 square centimeters. Find the area of each regular polygon described. Round your answers to the nearest tenth. 1. a hexagon with an apothem of 8.7 cm and 2. a pentagon with a perimeter of 54.49 m and sides that are each 10 cm long an apothem of 7.5 m 3. A regular octagon with an apothem 4.8 4. A square with a side 24 inches long and an centimeters long and a side 4 centimeters apothem 12 inches long long Find the apothem for each of the regular polygons below. Then find the perimeter and area for each figure. 5. 6. 7. a ________ a ________ a ________ P = ________ P = ________ P = ________ A ________ A ________ A ________ 8. The perimeter of a regular hexagon is 48 ft. 9. Ms. King wants to add a triangular deck in What is the area of this polygon? the yard behind her house. Each side is to be 18 feet long. Find the length of the railing that will fit completely around the deck. Then find the area of the deck. Find the area of the shaded region in the regular polygon. 10. 10 cm 4cm 11. 12. A regular pentagon with an apothem of 2 ft. 13. 14. 15. What is the side length of a regular 36-gon that 16. What is the perimeter of a regular hexagon that 2 has an area of 164,592 m and an apothem of has an area of √ in2 and an apothem of √ 228.6 m? in? 17. A regular hexagon has an area of approximately 18. A regular nonagon has an area of approximately 20 square centimeters. If the apothem measures 891 square centimeters. If each side measures 12 2.4 centimeters, find the approximate length of centimeters, find the approximate length of the each side. apothem .